Question

Solve the following quadratic equation for all values of xx in simplest form.
left parenthesis, x, plus, 10, right parenthesis, squared, minus, 14, equals, 11
(x+10)
2
−14=
11

Answer 1

To solve the quadratic equation \((x + 10)^2 - 14 = 11\), we can start by isolating the squared term.

1. Add 14 to both sides of the equation:
\[
(x + 10)^2 - 14 + 14 = 11 + 14
\]
\[
(x + 10)^2 = 25
\]

2. Next, we take the square root of both sides. Remember to consider both the positive and negative square roots:
\[
x + 10 = 5 \quad \text{or} \quad x + 10 = -5
\]

3. Solve for \(x\) in each case:

- For \(x + 10 = 5\):
\[
x = 5 - 10 = -5
\]

- For \(x + 10 = -5\):
\[
x = -5 - 10 = -15
\]

4. The solutions to the quadratic equation are:
\[
x = -5 \quad \text{and} \quad x = -15
\]

Thus, the final answers are:
\[
\boxed{-5} \text{ and } \boxed{-15}
\]