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

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)

Step-by-step 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)

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

answer: (-6,3)

step-by-step explanation: