(x-10)(x-10)=121

2 min read Jun 17, 2024

Solving the Equation (x-10)(x-10) = 121

This equation represents a quadratic equation in a slightly disguised form. Let's break down how to solve it:

Expansion: We can start by expanding the left side of the equation using the distributive property (FOIL method): (x-10)(x-10) = x² - 10x - 10x + 100 = x² - 20x + 100
Standard Form: Now the equation becomes: x² - 20x + 100 = 121
Simplifying: Subtracting 121 from both sides, we get: x² - 20x - 21 = 0

We now have a standard quadratic equation in the form ax² + bx + c = 0. There are several methods to solve this:

Factoring:
- Find two numbers that multiply to -21 and add up to -20. The numbers -21 and 1 satisfy these conditions.
- Factor the equation: (x - 21)(x + 1) = 0
- Set each factor to zero and solve for x:
  - x - 21 = 0 => x = 21
  - x + 1 = 0 => x = -1
Quadratic Formula:
- The quadratic formula provides the solution for any equation in the form ax² + bx + c = 0: x = (-b ± √(b² - 4ac)) / 2a
- In our case, a = 1, b = -20, and c = -21. Substituting these values into the formula: x = (20 ± √((-20)² - 4 * 1 * -21)) / 2 * 1 x = (20 ± √(400 + 84)) / 2 x = (20 ± √484) / 2 x = (20 ± 22) / 2
  - x = 21 or x = -1

Therefore, the solutions to the equation (x-10)(x-10) = 121 are x = 21 and x = -1.