(x-5)2=25-9x

2 min read Jun 17, 2024
(x-5)2=25-9x

Solving the Equation (x-5)^2 = 25 - 9x

This article will guide you through solving the equation (x-5)^2 = 25 - 9x step-by-step.

1. Expanding the Equation

First, we need to expand the left side of the equation by squaring the binomial:

(x-5)^2 = (x-5)(x-5) = x^2 - 10x + 25

Now the equation becomes: x^2 - 10x + 25 = 25 - 9x

2. Simplifying the Equation

Let's move all terms to the left side of the equation to make it easier to solve:

x^2 - 10x + 25 - 25 + 9x = 0

Simplifying further:

x^2 - x = 0

3. Factoring the Equation

We can factor out an 'x' from both terms:

x(x - 1) = 0

4. Solving for x

For the product of two factors to be zero, at least one of them must be zero. Therefore, we have two possible solutions:

  • x = 0
  • x - 1 = 0 => x = 1

5. Verification

We can verify our solutions by plugging them back into the original equation:

  • For x = 0: (0 - 5)^2 = 25 - 9(0) => 25 = 25 (This solution works)
  • For x = 1: (1 - 5)^2 = 25 - 9(1) => 16 = 16 (This solution also works)

Therefore, the solutions to the equation (x-5)^2 = 25 - 9x are x = 0 and x = 1.

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