10.2 Solving Equations by Using Square Roots

1. 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.

2. 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.”

4. x2 = 100 x = 10, -10 • d. 4x2 = 25 x = 5/2, - 5/2 • e. 49x2 = 16 x = 4/7, -4/7

8. b. Solve the equation • (x + 7)2 = 81 • x + 7 = 9 x + 7 = -9 • x = 2 x = -16

10. d. Solve the equation 4x2+ 13 = 253. • 4x2 = 240 • X2 = 60 • X = 7.75, -7.75

11. e. Solve the equation 5x2- 19 =231. • 5x2 = 250 • x2= 50 • X = 7.07, -7.07