Question

What are the solutions to the quadratic equation: (x-3)^2/5=20

Answer 1

To solve the quadratic equation \(\frac{(x-3)^2}{5} = 20\), we can start by eliminating the fraction.

1. Multiply both sides of the equation by 5:

\[
(x-3)^2 = 20 \cdot 5
\]

\[
(x-3)^2 = 100
\]

2. Next, take the square root of both sides. Remember to consider both the positive and negative square roots:

\[
x - 3 = \pm 10
\]

3. Now, we can solve for \(x\) in each case:

**Case 1:** \(x - 3 = 10\)

\[
x = 10 + 3
\]

\[
x = 13
\]

**Case 2:** \(x - 3 = -10\)

\[
x = -10 + 3
\]

\[
x = -7
\]

4. Therefore, the solutions to the quadratic equation \(\frac{(x-3)^2}{5} = 20\) are:

\[
\boxed{13} \quad \text{and} \quad \boxed{-7}
\]