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6.5 – Solving Equations with Quadratic Techniques. Quadratic equations are in the form: a x 2 + b x + c ,. Quadratic equations are in the form: a x 2 + b x + c , where a, b, & c are integers. Quadratic equations are in the form: a x 2 + b x + c , where a, b, & c are integers exs. . - PowerPoint PPT Presentation
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6.5 – Solving Equations with Quadratic Techniques
Quadratic equations are in the form:
ax2 + bx + c,
Quadratic equations are in the form:
ax2 + bx + c, where a, b, & c are integers
Quadratic equations are in the form:
ax2 + bx + c, where a, b, & c are integers
exs.
Quadratic equations are in the form:
ax2 + bx + c, where a, b, & c are integers
exs.
• x2 + 5x + 2
Quadratic equations are in the form:
ax2 + bx + c, where a, b, & c are integers
exs.
• x2 + 5x + 2
• 2x2 – 18x + 13
Quadratic equations are in the form:
ax2 + bx + c, where a, b, & c are integers
exs.
• x2 + 5x + 2
• 2x2 – 18x + 13
• x2 – 9
Quadratic equations are in the form:
ax2 + bx + c, where a, b, & c are integers
exs.
• x2 + 5x + 2
• 2x2 – 18x + 13
• x2 – 9
x2 + 0x – 9
Quadratic equations are in the form:ax2 + bx + c, where a, b, & c are integersexs.
• x2 + 5x + 2• 2x2 – 18x + 13• x2 – 9
x2 + 0x – 9• 2x2 + 8x
Quadratic equations are in the form:ax2 + bx + c, where a, b, & c are integersexs.
• x2 + 5x + 2• 2x2 – 18x + 13• x2 – 9
x2 + 0x – 9• 2x2 + 8x
2x2 + 8x + 0
Quadratic equations are in the form:ax2 + bx + c, where a, b, & c are integersexs.
• x2 + 5x + 2• 2x2 – 18x + 13• x2 – 9
x2 + 0x – 9• 2x2 + 8x
2x2 + 8x + 0NOTE: Must have the “x2” term to be a quadratic!
Ex. 1 Write each expression in quadratic form, if possible.
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
(x2)2
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
(x2)2 + 13(x2)
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
(x2)2 + 13(x2) + 36
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
(x2)2 + 13(x2) + 36
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
(x2)2 + 13(x2) + 36
b. 16x6 – 625
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
(x2)2 + 13(x2) + 36
b. 16x6 – 625
(4x3)2
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36
(x2)2 + 13(x2) + 36
b. 16x6 – 625
(4x3)2 – 625
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36
b. 16x6 – 625 (4x3)2 – 625
c. x½ – 9x¼ + 16
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36
b. 16x6 – 625 (4x3)2 – 625
c. x½ – 9x¼ + 16 (x¼)2
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36
b. 16x6 – 625 (4x3)2 – 625
c. x½ – 9x¼ + 16 (x¼)2 – 9(x¼)
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36
b. 16x6 – 625 (4x3)2 – 625
c. x½ – 9x¼ + 16 (x¼)2 – 9(x¼) + 16
Ex. 1 Write each expression in quadratic form, if possible.
a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36
b. 16x6 – 625 (4x3)2 – 625
c. x½ – 9x¼ + 16 (x¼)2 – 9(x¼) + 16
Ex. 2 Solve each equation.a. x4 = 16
Ex. 2 Solve each equation.a. x4 = 16
-16 -16
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 )(x2 ) = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 (x )(x ) = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0
x – 2 = 0 OR x + 2 = 0
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0
x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0
x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2
x = 2 OR x = -2
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0
x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2
x = 2 OR x = -2
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0
x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2
x = 2 OR x = -2
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x2 + 4 = 0
x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2
x = 2 OR x = -2
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x2 + 4 = 0
x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2
x = 2 OR x = -2
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x2 + 4 = 0
x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2 √x2 = √-4
x = 2 OR x = -2
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x2 + 4 = 0
x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2 √x2 = √-4
x = 2 OR x = -2 OR x = ±2i
Ex. 2 Solve each equation.a. x4 = 16
-16 -16 x4 – 16 = 0 (x2)2 – 16 = 0
( )( ) = 0(x2 – 4)(x2 + 4) = 0
x2 – 4 = 0 OR x2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x2 + 4 = 0
x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2 √x2 = √-4
x = 2 OR x = -2 OR x = ±2i
b. x4 + 11x2 + 18 = 0
b. x4 + 11x2 + 18 = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 )(x2 ) = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0 OR x2 + 2 = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0 OR x2 + 2 = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0 OR x2 + 2 = 0
(x + )(x + ) = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0
x2 + 9 = 0
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0
x2 + 9 = 0
-9 -9
b. x4 + 11x2 + 18 = 0
(x2)2 + 11(x2) + 18 = 0
( )( ) = 0
(x2 + 9)(x2 + 2) = 0
x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0
x2 + 9 = 0
-9 -9
x2 = -9
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 -9 -9
x2 = -9 √x2 = √-9
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 -9 -9
x2 = -9 √x2 = √-9
x = ±3i
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 -9 -9
x2 = -9 √x2 = √-9
x = ±3i
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 (x + )(x + ) = 0 x2 + 9 = 0 -9 -9
x2 = -9 √x2 = √-9
x = ±3i
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 OR x2 + 2 = 0 -9 -9
x2 = -9 √x2 = √-9
x = ±3i
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 OR x2 + 2 = 0 -9 -9 -2 -2
x2 = -9 √x2 = √-9
x = ±3i
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 OR x2 + 2 = 0 -9 -9 -2 -2
x2 = -9 OR x2 = -2 √x2 = √-9
x = ±3i
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 OR x2 + 2 = 0 -9 -9 -2 -2
x2 = -9 OR x2 = -2 √x2 = √-9 OR √x2 = √-2
x = ±3i
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 OR x2 + 2 = 0 -9 -9 -2 -2
x2 = -9 OR x2 = -2 √x2 = √-9 OR √x2 = √-2
x = ±3i OR x = ±i√2
b. x4 + 11x2 + 18 = 0 (x2)2 + 11(x2) + 18 = 0( )( ) = 0
(x2 + 9)(x2 + 2) = 0 x2 + 9 = 0 OR x2 + 2 = 0
( )( ) = 0 ( )( ) = 0 x2 + 9 = 0 OR x2 + 2 = 0 -9 -9 -2 -2
x2 = -9 OR x2 = -2 √x2 = √-9 OR √x2 = √-2
x = ±3i OR x = ±i√2
c. x½ – 6x¼ – 16 = 0
c. x½ – 6x¼ – 16 = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
(x¼ )(x¼ ) = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
(x¼ – 8)(x¼ + 2) = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0
( )( ) = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0
( )( ) = 0
x¼ – 8 = 0
c. x½ – 6x¼ – 16 = 0
(x¼)2 – 6(x¼) – 16 = 0
( )( ) = 0
(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0
( )( ) = 0
x¼ – 8 = 0
+8 +8
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0
x¼ – 8 = 0 +8 +8 x¼ = 8
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0
x¼ – 8 = 0 +8 +8 x¼ = 8 (x¼)4 = (8)4
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0
x¼ – 8 = 0 +8 +8 x¼ = 8 (x¼)4 = (8)4 x = 4096
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0
x¼ – 8 = 0 +8 +8 x¼ = 8 (x¼)4 = (8)4 x = 4096
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0 ( )( ) = 0
x¼ – 8 = 0 +8 +8 x¼ = 8 (x¼)4 = (8)4 x = 4096
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0 ( )( ) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 +8 +8 x¼ = 8 (x¼)4 = (8)4 x = 4096
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0 ( )( ) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 +8 +8 -2 -2 x¼ = 8 (x¼)4 = (8)4 x = 4096
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0 ( )( ) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 +8 +8 -2 -2 x¼ = 8 OR x¼ = -2 (x¼)4 = (8)4 x = 4096
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0 ( )( ) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 +8 +8 -2 -2 x¼ = 8 OR x¼ = -2 (x¼)4 = (8)4 OR (x¼)4 = (-2)4 x = 4096
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0 ( )( ) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 +8 +8 -2 -2 x¼ = 8 OR x¼ = -2 (x¼)4 = (8)4 OR (x¼)4 = (-2)4 x = 4096 OR x = 16
c. x½ – 6x¼ – 16 = 0 (x¼)2 – 6(x¼) – 16 = 0( )( ) = 0(x¼ – 8)(x¼ + 2) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 ( )( ) = 0 ( )( ) = 0
x¼ – 8 = 0 OR x¼ + 2 = 0 +8 +8 -2 -2 x¼ = 8 OR x¼ = -2 (x¼)4 = (8)4 OR (x¼)4 = (-2)4 x = 4096 OR x = 16
