Question

solve x^2+6x-7 by completing the square

Answer 1

To solve the quadratic equation \(x^2 + 6x - 7\) by completing the square, follow these steps:

1. **Move the constant to the other side**:
\[
x^2 + 6x = 7
\]

2. **Take half of the coefficient of \(x\)** (which is \(6\)), square it, and add it to both sides. Half of \(6\) is \(3\), and \(3^2 = 9\).

Add \(9\) to both sides:
\[
x^2 + 6x + 9 = 7 + 9
\]
\[
x^2 + 6x + 9 = 16
\]

3. **Rewrite the left side as a square**:
\[
(x + 3)^2 = 16
\]

4. **Take the square root of both sides**:
\[
x + 3 = \pm 4
\]

5. **Solve for \(x\)**:
- For the positive case:
\[
x + 3 = 4 \implies x = 4 - 3 = 1
\]
- For the negative case:
\[
x + 3 = -4 \implies x = -4 - 3 = -7
\]

Thus, the solutions are:
\[
x = 1 \quad \text{and} \quad x = -7
\]