Question

x^2+6x+8=0 by completing the square

Answer 1

To solve the quadratic equation \(x^2 + 6x + 8 = 0\) by completing the square, follow these steps:

1. **Move the constant term to the other side of the equation**:
\[
x^2 + 6x = -8
\]

2. **Complete the square**. To do this, take the coefficient of \(x\) (which is 6), divide it by 2 to get 3, and then square it to get 9.

3. **Add and subtract this square inside the equation**:
\[
x^2 + 6x + 9 = -8 + 9
\]

This simplifies to:
\[
x^2 + 6x + 9 = 1
\]

4. **Now, rewrite the left side as a perfect square**:
\[
(x + 3)^2 = 1
\]

5. **Take the square root of both sides**:
\[
x + 3 = \pm 1
\]

6. **Solve for \(x\)** by isolating it:
\[
x + 3 = 1 \quad \Rightarrow \quad x = 1 - 3 \quad \Rightarrow \quad x = -2
\]
\[
x + 3 = -1 \quad \Rightarrow \quad x = -1 - 3 \quad \Rightarrow \quad x = -4
\]

Thus, the solutions to the equation \(x^2 + 6x + 8 = 0\) are:
\[
\boxed{-2} \quad \text{and} \quad \boxed{-4}
\]