(x-5)^2+7=2x

2 min read Jun 17, 2024

Solving the Equation (x-5)^2 + 7 = 2x

This article will guide you through the steps to solve the equation (x-5)² + 7 = 2x. We will use algebraic manipulation to isolate the variable 'x' and find the solution.

Step 1: Expand the Square

Begin by expanding the square on the left side of the equation. Remember that (a-b)² = a² - 2ab + b². Applying this to our equation:

(x-5)² + 7 = 2x x² - 10x + 25 + 7 = 2x

Step 2: Simplify and Rearrange

Combine the constant terms and move all terms to one side of the equation.

x² - 10x + 32 = 2x x² - 12x + 32 = 0

Step 3: Factor the Quadratic Equation

Now, we have a quadratic equation in standard form (ax² + bx + c = 0). Let's factor it:

(x-8)(x-4) = 0

Step 4: Solve 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 - 8 = 0 or x - 4 = 0

Solving for x in each case:

x = 8 or x = 4

Conclusion

The solutions to the equation (x-5)² + 7 = 2x are x = 8 and x = 4.