Solve the following quadratic equation for all values of xx in simplest form.

Question

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: \[ \boxed{-5} \text{ and } \boxed{-15} \]