Question

Solve the following quadratic equation for all values of xx in simplest form.
5, left parenthesis, x, minus, 3, right parenthesis, squared, equals, 45
5(x−3)
2
=
45

Answer 1

To solve the equation \( 5(x - 3)^2 = 45 \), follow these steps:

1. **Divide both sides by 5**:

\[
(x - 3)^2 = \frac{45}{5}
\]
\[
(x - 3)^2 = 9
\]

2. **Take the square root of both sides**:

\[
x - 3 = \pm 3
\]

3. **Solve for \( x \)** for both the positive and negative scenarios:

- For the positive case:
\[
x - 3 = 3
\]
\[
x = 3 + 3 = 6
\]

- For the negative case:
\[
x - 3 = -3
\]
\[
x = -3 + 3 = 0
\]

4. **Final solutions**:

The solutions to the quadratic equation \( 5(x - 3)^2 = 45 \) are

\[
\boxed{0} \quad \text{and} \quad \boxed{6}
\]