Question

Solve x^2 + 8x = 10 to complete the square

Answer 1

To solve the equation \( x^2 + 8x = 10 \) by completing the square, follow these steps:

1. **Move the constant to the other side:**
\[
x^2 + 8x - 10 = 0
\]

2. **Isolate the \(x^2 + 8x\) term:**
\[
x^2 + 8x = 10
\]

3. **Complete the square:**
- Take the coefficient of \(x\), which is 8, divide it by 2 to get 4, and then square it to get \(16\).
- Add and subtract \(16\) on the left side:
\[
x^2 + 8x + 16 - 16 = 10
\]
This simplifies to:
\[
(x + 4)^2 - 16 = 10
\]

4. **Rearranging gives:**
\[
(x + 4)^2 = 26
\]

5. **Taking the square root of both sides:**
\[
x + 4 = \pm \sqrt{26}
\]

6. **Solving for \(x\):**
\[
x = -4 \pm \sqrt{26}
\]

So the solutions are:
\[
x = -4 + \sqrt{26} \quad \text{and} \quad x = -4 - \sqrt{26}
\]