10.2 Solving Equations by Using Square Roots

Objectives: Solve equations of the form ax2 = k. Solve equations of the form ax2 = k where x

is replaced by an algebraic expression.Standard Addressed: 2.8.11.N. Solve

quadratic equations.

The equation x2 = 9 can be stated as the question, “What number multiplied by itself is 9?” There are two such numbers, 3 and -3. Each of these is called a square root of 9. The positive square root of a number is called the principal square root. The principal square root of a number is indicated by the radical sign. In general, if x2= k and k > 0, then x = You can write this as , which is read as “plus or minus the square root of k.”

x2 = 100 x = 10, -10

d. 4x2 = 25 x = 5/2, - 5/2

e. 49x2 = 16 x = 4/7, -4/7

(x + 7)2 = 81 x + 7 = 9 x + 7 = -9 x = 2 x = -16

b. Solve the equation

4x2 = 240 X2 = 60 X = 7.75, -7.75

d. Solve the equation 4x2 + 13 = 253.

5x2 = 250 x2 = 50 X = 7.07, -7.07

e. Solve the equation 5x2 - 19 =231.