Q1 Solve the following quadratic equation using square roots: (x-5)^2= 49

Answer 1

To solve the quadratic equation \((x - 5)^2 = 49\) using square roots, follow these steps:

1. Take the square root of both sides:

\[ \sqrt{(x - 5)^2} = \pm \sqrt{49} \]

This simplifies to:

\[ x - 5 = \pm 7 \]

2. Now, solve for \(x\) in both cases:

Case 1:

\[ x - 5 = 7 \] Adding 5 to both sides gives:

\[ x = 7 + 5 = 12 \]

Case 2:

\[ x - 5 = -7 \] Adding 5 to both sides gives:

\[ x = -7 + 5 = -2 \]

3. Therefore, the solutions to the equation \((x - 5)^2 = 49\) are:

\[ x = 12 \quad \text{and} \quad x = -2 \]