Question

Solve the quadratic equation.

x^2+9x-36=0

answers:

x=3 or 12

x=3 or-12

x=6 or-6

no real solution

Answer 1

To solve the quadratic equation \( x^2 + 9x - 36 = 0 \), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this equation, \( a = 1 \), \( b = 9 \), and \( c = -36 \).

1. First, calculate the discriminant:

\[
b^2 - 4ac = 9^2 - 4 \cdot 1 \cdot (-36) = 81 + 144 = 225
\]

2. Now, substitute back into the quadratic formula:

\[
x = \frac{-9 \pm \sqrt{225}}{2 \cdot 1}
\]

3. Since \( \sqrt{225} = 15 \), we find:

\[
x = \frac{-9 \pm 15}{2}
\]

4. This gives us two possible solutions:

\[
x = \frac{-9 + 15}{2} = \frac{6}{2} = 3
\]

\[
x = \frac{-9 - 15}{2} = \frac{-24}{2} = -12
\]

Thus, the solutions to the equation \( x^2 + 9x - 36 = 0 \) are:
\[
x = 3 \quad \text{or} \quad x = -12
\]

So the correct answer is:
**x = 3 or -12**.