Solve the following quadratic equation using square roots: (x−18)^2=196 .

Answer 1

To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, follow these steps:

1. Take the square root of both sides of the equation: \[ x - 18 = \pm \sqrt{196} \]

2. Calculate \(\sqrt{196}\): \[ \sqrt{196} = 14 \]

3. Now rewrite the equation: \[ x - 18 = \pm 14 \]

4. This gives us two separate equations to solve: \[ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 \]

5. Solve the first equation: \[ x - 18 = 14 \quad \Rightarrow \quad x = 14 + 18 = 32 \]

6. Solve the second equation: \[ x - 18 = -14 \quad \Rightarrow \quad x = -14 + 18 = 4 \]

Thus, the solutions to the equation \((x - 18)^2 = 196\) are: \[ x = 32 \quad \text{and} \quad x = 4 \]