2%3D25-9x.jpeg "(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.