Question

Solving Square Root Worksheet (x - k)^2 Part 2

4. 3(x - 2)^2 = 40

5. -2(x - 1)^2 = 36

6. 4(x - 1)^2 = 8

Answer 1

4. x = 2 + 2sqrt(10/3), 2- 2sqrt(10/3)

5. No real solutions

x = 1 + 3sqrt(2) i, 1 - 3sqrt(2) i,

6. x = 1 + sqrt(2), 1 - sqrt(2)

Explanation:

4. 3(x - 2)² = 40

(x - 2)² = 40/3

(x - 2) = +/- sqrt(40/3)

x - 2 = +/- 2sqrt(10/3)

x = 2 +/- 2sqrt(10/3)

5. -2(x - 1)² = 36

(x - 1)² = -18

A perfect square can never be negative for real values of x

(x - 1) = +/- i × sqrt(18)

x - 1 = +/- i × 3sqrt(2)

x = 1 +/- i × 3sqrt(2)

6. 4(x - 1)² = 8

(x - 1)² = 2

x - 1 = +/- sqrt(2)

x = 1 +/- sqrt(2)