Question

Create a list of steps, in order, that will solve the following equation.
\[2(x+2)^2-5=93\]

Answer 1

To solve the equation \(2(x+2)^2 - 5 = 93\), follow these steps:

1. **Add 5 to both sides of the equation** to isolate the term with the square:
\[
2(x+2)^2 = 93 + 5
\]
\[
2(x+2)^2 = 98
\]

2. **Divide both sides by 2** to simplify:
\[
(x+2)^2 = \frac{98}{2}
\]
\[
(x+2)^2 = 49
\]

3. **Take the square root of both sides** to solve for \(x + 2\):
\[
x + 2 = \pm 7
\]

4. **Solve for \(x\)** by subtracting 2 from both possible equations:
- For the positive root:
\[
x + 2 = 7 \implies x = 7 - 2 \implies x = 5
\]
- For the negative root:
\[
x + 2 = -7 \implies x = -7 - 2 \implies x = -9
\]

5. **Write the final solutions**:
\[
x = 5 \quad \text{or} \quad x = -9
\]

Thus, the complete solution process results in \(x = 5\) or \(x = -9\).