Question

solve the following quadratic equation using square roots: (X+36)^2 - 38 = 251

Answer 1

To solve the quadratic equation \((X + 36)^2 - 38 = 251\) using square roots, we first need to isolate the squared term. Here are the steps to solve the equation:

1. Start with the original equation:
\[
(X + 36)^2 - 38 = 251
\]

2. Add 38 to both sides to isolate the squared term:
\[
(X + 36)^2 = 251 + 38
\]
\[
(X + 36)^2 = 289
\]

3. Now, take the square root of both sides:
\[
X + 36 = \pm \sqrt{289}
\]

4. Since \(\sqrt{289} = 17\), we have:
\[
X + 36 = 17 \quad \text{or} \quad X + 36 = -17
\]

5. Now, solve for \(X\) in both cases:
- For \(X + 36 = 17\):
\[
X = 17 - 36 = -19
\]
- For \(X + 36 = -17\):
\[
X = -17 - 36 = -53
\]

6. Thus, the solutions to the quadratic equation are:
\[
X = -19 \quad \text{and} \quad X = -53
\]

The final answer is:
\[
X = -19 \quad \text{or} \quad X = -53
\]