QUESTION IMAGE
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})
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 $x=1-5\sqrt{2}$
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
$x=1+5\sqrt{2}$, $x=1-5\sqrt{2}$