Question

given \\((x - 1)^2 = 50\\), select the values of \\(x\\).

\\(x = -49\\)
\\(x = 51\\)
\\(x = 1 + 5\sqrt{2}\\)
\\(x = 1 - 5\sqrt{2}\\)

Explanation:

Step1: Write the equation

$$(x - 1)^2 = 50$$

Step2: Take square root

$$x - 1 = \pm\sqrt{50}$$

Step3: Simplify the radical

$$x - 1 = \pm 5\sqrt{2}$$

Step4: Solve for x

$$x = 1 \pm 5\sqrt{2}$$

Answer:

\(x = 1 + 5\sqrt{2}\), \(x = 1 - 5\sqrt{2}\)