Question

solve the following quadratic equation for all values of x in simplest form.
(x + 10)^2 - 14 = 11

Explanation:

Step1: Isolate the squared term

Add 14 to both sides of the equation:
$$(x + 10)^2 - 14 + 14 = 11 + 14$$
Simplify to get:
$$(x + 10)^2 = 25$$

Step2: Take square roots

Take the square root of both sides. Remember that taking the square root of a number gives two solutions (positive and negative):
$$x + 10 = \pm\sqrt{25}$$
Since $\sqrt{25} = 5$, we have:
$$x + 10 = \pm 5$$

Step3: Solve for \(x\)

Case 1: When \(x + 10 = 5\)
Subtract 10 from both sides:
$$x = 5 - 10$$
$$x = -5$$
Case 2: When \(x + 10 = -5\)
Subtract 10 from both sides:
$$x = -5 - 10$$
$$x = -15$$

Answer:

\(x = -5\) or \(x = -15\)