Question

Solve (x+5)²=4 using square roots

x=___ and x = ____

Answer 1

To solve the equation \((x+5)²=4\) using square roots, follow these steps:

1. Take the square root of both sides of the equation. Remember to consider both the positive and negative roots:
\[
x + 5 = \pm 2
\]

2. This gives us two separate equations to solve:
- \(x + 5 = 2\)
- \(x + 5 = -2\)

3. Solve each equation:

For \(x + 5 = 2\):
\[
x = 2 - 5
\]
\[
x = -3
\]

For \(x + 5 = -2\):
\[
x = -2 - 5
\]
\[
x = -7
\]

So the solutions are:
\[
x = -3 \quad \text{and} \quad x = -7
\]

Thus, you can fill in:

x = -3 and x = -7.