Question

given ((x - 1)^2 = 50), select the values of (x). (square) (x = -49) (square) (x = 51) (square) (x = 1 + 5sqrt{2}) (square) (x = 1 - 5sqrt{2})

Explanation:

Step1: Take square roots of both sides

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

Step2: Simplify the square root

$\sqrt{50} = \sqrt{25\times2} = 5\sqrt{2}$, so:
$$x-1 = \pm5\sqrt{2}$$

Step3: Solve for x

Add 1 to both sides:
$$x = 1 \pm5\sqrt{2}$$
This gives two solutions: $x=1+5\sqrt{2}$ and $x=1-5\sqrt{2}$

Answer:

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