154k views
0 votes
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

2 Answers

4 votes

Answer:

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)

User Saa
by
7.6k points
5 votes

Answer:

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!

User Cschwan
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories