Question

Solving Square Roots Worksheet (x - k)^2 : Part 1

1. 2(x + 7)^2 = 16

2. (x - 3)^2 = -12

3. -5(n - 3)^2 = 10

Answer 1

1. x = 2sqrt(2) - 7, -2sqrt(2) - 7

2. No real solutions

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

3. No real solutions

n = 3 + sqrt(2) i, 3 - sqrt(2) i

Explanation:

1. 2(x + 7)² = 16

(x + 7)² = 8

x + 7 = +/- sqrt(8) = +/- 2sqrt(2(

x = 2sqrt(2) - 7, -2sqrt(2) - 7

2. (x - 3)² = -12

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

(x - 3) = +/- i × sqrt(12)

x - 3 = +/- i × 2sqrt(3)

x = 3 +/- i × 2sqrt(3)

3. -5(n - 3)² = 10

(n - 3)² = -2

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

n - 3 = +/- i × sqrt(2)

n = 3 +/- i × sqrt(2)

Answer 2

1. x = +/- 2
`√(2)` - 7

2. x =
`3` +/-
`2i√(3)`

3. n =
`2` +/-
`i√(2)`

Explanation:

1. Divide both sides by 2: (x + 7)^2 = 8

Square root both sides: x + 7 = +/- 2
`√(2)`

Subtract 7 from both sides: x = +/- 2
`√(2)` - 7

2. Square root both sides: x - 3 =
`√(-12)`

Since there is a negative inside the radical, we need to have an imaginary number:
`i=√(-1)` . So,
`√(-12) =i√(12) =2i√(3)`

Add 3 to both sides: x =
`3` +/-
`2i√(3)`

3. Divide by -5 from both sides: (n - 2)^2 = -2

Square root both sides: n - 2 =
`√(-2)`

Again, we have to use i:
`n-2=√(-2) =i√(2)`

Add 2 to both sides: n =
`2` +/-
`i√(2)`

Hope this helps!