Solve (x-1)^2 = 16
show steps
To solve the equation (x-1)^2 = 16, you can follow these steps:
Step 1: Expand the equation:
(x-1)^2 = 16
(x-1)(x-1) = 16
x^2 - 2x + 1 = 16
Step 2: Subtract 16 from both sides to isolate x:
x^2 - 2x + 1 - 16 = 16 - 16
x^2 - 2x - 15 = 0
Step 3: Now, let's factor the equation:
(x-5)(x+3)=0
Step 4: Apply the zero product property:
x-5 = 0 or x+3 = 0
Step 5: Solve for x in each equation:
x = 5 or x = -3
So, the solutions to the equation (x-1)^2 = 16 are x = 5 and x = -3.