Solving Quadratic Equations

Review of Solving Quadratic Equations

ax2 +bx +c = 0When the equation is equal to zero, solve by factoring if you can. You can test if it can factor by calculating b2 – 4ac

x 2 5x 6

x 2 5x 6 0

(x 6)(x 1) 0

x 6 0 & x 10

x 6 x 1

Solve Quadratic Eq. By Factoring

1. Set Eq = 0 2. Factor 3. Set Each Factor = 04. Check Answers by Putting into

Original Eq.

x 2 5x 6

Solving Square Trinomials Equations

ax2 +bx +c = Sometimes the equation will factor in a special way: ( + )2 = This can sometimes happen even before you make the equation equal zero.

49442 xxSolve with Perfect Square Binomial

72

49)2(

49)2(

2

2

x

x

x

x 2 7

x 9

x 2 7

x 5

1. Get Perfect Squares on Both Sides of Equation.

2. Take Square Root of Perfect Squares

3. Solve Positive Number & Neg. Number

4. Check Answers by Putting into Original Eq.

50962 xxSolve with Perfect Square Binomial

253

252253

50)3(

50)3(

2

2

x

x

x

x

253x

1. Get Perfect Squares Binomial. 2. Take Square Root of Both Sides

of Eq 3. Simplify4. Check Answers by Putting into

Original Eq.

253 x

How can we recognize these special cases?

The coefficient of the quadratic term is squareThe constant term is squareThe coefficient of the linear term is double the product

of the square root of the coefficient of the quadratic and the square root of the constant term.

50962 xx

49442 xx

7364162 xx

819124 2 xx

6316249 2 xx

You try:

5091025 2 xx

7225309 2 xx

9664162 xx

811816 2 xx