(x-1)^2-16=-12

2 min read Jun 17, 2024

Solving the Equation (x-1)^2 - 16 = -12

This article will walk through the steps involved in solving the equation (x-1)^2 - 16 = -12.

Step 1: Isolate the Squared Term

To begin, we need to isolate the term containing the squared expression, (x-1)^2. To do this, add 16 to both sides of the equation:

(x-1)^2 - 16 + 16 = -12 + 16 (x-1)^2 = 4

Step 2: Take the Square Root of Both Sides

Now, take the square root of both sides of the equation. Remember that when taking the square root, we need to consider both positive and negative solutions:

√[(x-1)^2] = ±√4 x-1 = ±2

Step 3: Solve for x

Finally, we need to solve for x by isolating it in each of the two possible equations:

Case 1: x - 1 = 2 x = 2 + 1 x = 3

Case 2: x - 1 = -2 x = -2 + 1 x = -1

Solution

Therefore, the solutions to the equation (x-1)^2 - 16 = -12 are x = 3 and x = -1.