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(x-12)^2=(9+x)^2

2 min read Jun 17, 2024
(x-12)^2=(9+x)^2

Solving the Equation: (x-12)^2 = (9+x)^2

This equation presents a quadratic equation that can be solved using various methods. Let's break down the steps to find the solutions for 'x'.

1. Expanding the Squares

The first step is to expand both sides of the equation using the formula (a-b)^2 = a^2 - 2ab + b^2 :

  • Left Side: (x-12)^2 = x^2 - 2(x)(12) + 12^2 = x^2 - 24x + 144
  • Right Side: (9+x)^2 = 9^2 + 2(9)(x) + x^2 = 81 + 18x + x^2

Now, our equation becomes: x^2 - 24x + 144 = 81 + 18x + x^2

2. Simplifying the Equation

Next, let's simplify the equation by bringing all terms to one side:

  • x^2 - 24x + 144 - 81 - 18x - x^2 = 0
  • -42x + 63 = 0

3. Solving for 'x'

We now have a simple linear equation. Let's solve for 'x':

  • -42x = -63
  • x = -63 / -42
  • x = 3/2

Conclusion

Therefore, the solution to the equation (x-12)^2 = (9+x)^2 is x = 3/2.

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