Question

Solve the following quadratic equation for all values of xx in simplest form.
left parenthesis, 5, x, plus, 6, right parenthesis, squared, plus, 24, equals, 33
(5x+6)
2
+24=
33

Answer 1

To solve the quadratic equation \((5x + 6)^2 + 24 = 33\), we can follow these steps:

1. **Isolate the squared term**:
\[
(5x + 6)^2 + 24 - 24 = 33 - 24
\]
Simplifying this gives:
\[
(5x + 6)^2 = 9
\]

2. **Take the square root of both sides**:
\[
5x + 6 = \pm 3
\]

This results in two separate equations to solve:
1. \(5x + 6 = 3\)
2. \(5x + 6 = -3\)

3. **Solve each equation**:

- For the first equation \(5x + 6 = 3\):
\[
5x = 3 - 6
\]
\[
5x = -3
\]
\[
x = -\frac{3}{5}
\]

- For the second equation \(5x + 6 = -3\):
\[
5x = -3 - 6
\]
\[
5x = -9
\]
\[
x = -\frac{9}{5}
\]

4. **Final solutions**:
The values of \(x\) that solve the equation are:
\[
x = -\frac{3}{5} \quad \text{and} \quad x = -\frac{9}{5}
\]