Question

solve for \\(x\\) in the equation \\(x^2 + 20x + 100 = 36\\).

\\(x = -16\\) or \\(x = -4\\)
\\(x = -10\\)
\\(x = -8\\)
\\(x = 4\\) or \\(x = 16\\)

Explanation:

Step1: Write the equation

$$x^2 + 20x + 100 = 36$$

Step2: Factor the perfect square trinomial

$$(x + 10)^2 = 36$$

Step3: Take the square root

$$x + 10 = \pm 6$$

Step4: Solve for \(x\)

$$x = -10 \pm 6$$

Step5: Calculate both solutions

$$x = -16 \text{ or } x = -4$$

Answer:

\(x = -16\) or \(x = -4\)