Question

what is the positive solution to this equation?
x^2 + 5x - 36 = 0

Answer 1

To find the positive solution to the equation \( x^2 + 5x - 36 = 0 \), you can use the quadratic formula:

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

In this equation, the coefficients are:
- \( a = 1 \)
- \( b = 5 \)
- \( c = -36 \)

Plugging these values into the quadratic formula gives:

1. Calculate the discriminant (\( b^2 - 4ac \)):
\[
b^2 - 4ac = 5^2 - 4 \cdot 1 \cdot (-36) = 25 + 144 = 169
\]

2. Now, apply the quadratic formula:
\[
x = \frac{{-5 \pm \sqrt{169}}}{2 \cdot 1}
\]
\[
x = \frac{{-5 \pm 13}}{2}
\]

3. This gives two potential solutions:
\[
x_1 = \frac{{-5 + 13}}{2} = \frac{8}{2} = 4
\]
\[
x_2 = \frac{{-5 - 13}}{2} = \frac{-18}{2} = -9
\]

The positive solution to the equation \( x^2 + 5x - 36 = 0 \) is:

\[
\boxed{4}
\]