Question

What is the positive solution to this equation?



`x^{2}+5x\ -\ 36=0`

Answer 1

To solve the quadratic equation \( x^2 + 5x - 36 = 0 \), we can use the quadratic formula, which is given by:

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

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

First, we calculate the discriminant \( b^2 - 4ac \):

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

Now, we apply the quadratic formula:

\[
x = \frac{-5 \pm \sqrt{169}}{2 \cdot 1} = \frac{-5 \pm 13}{2}
\]

This results in two possible solutions:

1. Using the positive root:

\[
x = \frac{-5 + 13}{2} = \frac{8}{2} = 4
\]

2. Using the negative root:

\[
x = \frac{-5 - 13}{2} = \frac{-18}{2} = -9
\]

Since we are looking for the positive solution, the answer is:

\[
\boxed{4}
\]