Question

Solve the following quadratic equation for all values of xx in simplest form.
5, left parenthesis, x, plus, 3, right parenthesis, squared, minus, 3, equals, 42
5(x+3)
2
−3=
42

Answer 1

To solve the equation \( 5(x + 3)^2 - 3 = 42 \), we will follow these steps:

1. **Isolate the quadratic term**:
\[
5(x + 3)^2 - 3 = 42
\]
Add 3 to both sides:
\[
5(x + 3)^2 = 45
\]

2. **Divide by 5**:
\[
(x + 3)^2 = 9
\]

3. **Take the square root**:
Taking the square root of both sides gives us two equations:
\[
x + 3 = 3 \quad \text{or} \quad x + 3 = -3
\]

4. **Solve for \( x \)**:
- For \( x + 3 = 3 \):
\[
x = 3 - 3 = 0
\]
- For \( x + 3 = -3 \):
\[
x = -3 - 3 = -6
\]

5. **Final Solutions**:
The solutions for the quadratic equation are:
\[
x = 0 \quad \text{and} \quad x = -6
\]

Thus, the values of \( x \) in simplest form are \( \boxed{0} \) and \( \boxed{-6} \).