Question

Solve x2 + 12x = –20 by completing the square.

Add (StartFraction b Over 2 EndFraction) squared to both sides of the equation. The value of (StartFraction b Over 2 EndFraction) squared in this equation is
.
Write the left side of the equation as a binomial squared. The left side of the equation becomes (
)2.
Use the square root property of equality.
Isolate the variable: x =

Answer 1

To solve the equation \( x^2 + 12x = -20 \) by completing the square, follow these steps:

1. **Move the constant term to the other side**:
\[
x^2 + 12x + 20 = 0
\]
(We can actually just keep the equation \( x^2 + 12x = -20 \) and add 20 to both sides later, but moving it here clarifies the next step.)

2. **Identify \( b \)**:
In the equation \( x^2 + 12x \), \( b = 12 \).

3. **Calculate \( \left( \frac{b}{2} \right)^2 \)**:
\[
\left( \frac{12}{2} \right)^2 = 6^2 = 36
\]

4. **Add \( \left( \frac{b}{2} \right)^2 \) to both sides of the equation**:
\[
x^2 + 12x + 36 = -20 + 36
\]
\[
x^2 + 12x + 36 = 16
\]

5. **Write the left side as a binomial squared**:
\[
(x + 6)^2 = 16
\]

6. **Use the square root property of equality**:
\[
x + 6 = \pm 4
\]

7. **Isolate the variable**:
- For \( x + 6 = 4 \):
\[
x = 4 - 6 = -2
\]
- For \( x + 6 = -4 \):
\[
x = -4 - 6 = -10
\]

Thus, the solutions to the equation \( x^2 + 12x = -20 \) are \( x = -2 \) and \( x = -10 \).