Question

Solve this quadratic equation by completing the square.
x2+8x=10
0 x=-8+V26
0 x=-4 ÷ V10
0 x=-4÷26
0 x=-8 + V10

Answer 1

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

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

2. **Complete the square**:
To complete the square, take half of the coefficient of \( x \), square it, and add it to both sides. The coefficient of \( x \) is 8, half of 8 is 4, and \( 4^2 = 16 \).

Add 16 to both sides:
\[
x^2 + 8x + 16 = 10 + 16
\]
\[
x^2 + 8x + 16 = 26
\]

3. **Rewrite the left side as a square**:
\[
(x + 4)^2 = 26
\]

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

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

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

From the options you've provided, the correct answer would be:
\[
x = -4 + \sqrt{26}
\]