2%3D169-brainly.jpeg "(x-4)2=169 Brainly")
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:
- x = 4 + 13 = 17
- x = 4 - 13 = -9
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.