Question

Solving Square Root Worksheet (x - k)^2 Part 3

7. 4(x + 2)^2 + 320 = 0

8. 7(x - 4)^2 - 18 = 10

9. -2(x + 2)^2 - 5 = 8

10. 1/5(t + 3)^2 = 7

Answer 1

7. -2 + 4sqrt(5) i, -2 - 4sqrt(5) i

8. x = 2, 6

9. x = -2 + sqrt(13/2) i, -2 - sqrt(13/2) i

10. t = -3 + sqrt(35), -3 - sqrt(35)

Explanation:

7. 4(x + 2)² + 320 = 0

(x + 2)² = -80

x + 2 = +/- i × sqrt(80)

x + 2 = +/- i × 4sqrt(5)

x = -2 +/- i × 4sqrt(5)

8. 7(x - 4)² - 18 = 10

(x - 4)² = 4

x - 4 = +/- 2

x = 2, 6

9. -2(x + 2)² - 5 = 8

(x + 2)² = -13/2

(x + 2) = +/- i × sqrt(13/2)

x = -2 +/- i × sqrt(13/2)

10. 1/5(t + 3)² = 7

(t + 3)² = 35

t + 3 = +/- sqrt(35)

t = -3 +/- sqrt(35)

Answer 2

7. x = -2 +/-
`4i√(5)`

8. x = 2 or x = 6

9. x = -2 +/-
`(√(26) )/(2) i`

10. t = -3 +/-
`√(35)`

Explanation:

7. Subtract 320 from both sides: 4(x + 2)^2 = -320

Divide by 4: (x + 2)^2 = -80

Square root both sides: x + 2 = +/-
`√(-80)`. We need to add the imaginary i to this: +/-
`√(-80)` = +/-
`i√(80)` = +/-
`4i√(5)`

Subtract 2 from both sides: x = -2 +/-
`4i√(5)`

8. Add 18 to both sides: 7(x - 4)^2 = 28

Divide by 7: (x - 4)^2 = 4

Square root both sides: x - 4 = +/- 2

Add 4 to both sides: x = 4 +/- 2 ⇒ x = 2 or x = 6

9. Add 5 to both sides: -2(x + 2)^2 = 13

Divide by -2: (x + 2)^2 = -13/2

Square root both sides: x + 2 = +/-
`√(-13/2)`. We again need i: +/-
`√(-13/2)` = +/-
`i√(13/2) =` +/-
`(√(26) )/(2) i`

Subtract 2 from both sides: x = -2 +/-
`(√(26) )/(2) i`

10. Multiply by 5 on both sides: (t + 3)^2 = 35

Square root both sides: t + 3 = +/-
`√(35)`

Subtract 3: t = -3 +/-
`√(35)`

Hope this helps!