(x-4)2=169 Brainly

2 min read Jun 17, 2024

Solving the Equation (x - 4)² = 169

This equation is a quadratic equation in disguise. Let's break it down step-by-step to find the solutions for x.

1. Take the Square Root of Both Sides:

The first step is to get rid of the square on the left-hand side. We do this by taking the square root of both sides of the equation:

√[(x - 4)²] = ±√169

2. Simplify:

The square root of (x - 4)² is simply (x - 4). The square root of 169 is 13. Remember that we need to consider both positive and negative roots:

x - 4 = ±13

3. Isolate x:

To isolate x, we add 4 to both sides of the equation:

x = 4 ± 13

4. Solve for x:

Now we have two possible solutions:

Therefore, the solutions to the equation (x - 4)² = 169 are x = 17 and x = -9.

Key Points:

Remember to consider both positive and negative roots when taking the square root of a number.
Always check your answers by substituting them back into the original equation to ensure they are valid solutions.