(x - 3)^2/5 = 20

Answer 1

To solve the equation \(\frac{(x - 3)^2}{5} = 20\), follow these steps:

1. Multiply both sides by 5 to eliminate the fraction:

   \[ (x - 3)^2 = 20 \times 5 \] \[ (x - 3)^2 = 100 \]

2. Take the square root of both sides:

   \[ x - 3 = \pm 10 \]

3. Solve for \(x\) by considering both cases:

   • Case 1: \[ x - 3 = 10 \implies x = 10 + 3 = 13 \]

   • Case 2: \[ x - 3 = -10 \implies x = -10 + 3 = -7 \]

Thus, the solutions are

\[ x = 13 \quad \text{and} \quad x = -7. \]

So, the final answer is:

\[ x = 13 \quad \text{or} \quad x = -7. \]