(2x-3)^2=4x+5

2 min read Jun 16, 2024

Solving the Equation (2x-3)^2 = 4x + 5

This article will guide you through the steps of solving the equation (2x - 3)^2 = 4x + 5.

First, we need to expand the left side of the equation by applying the square:

(2x - 3)^2 = (2x - 3)(2x - 3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9

Now, our equation becomes: 4x^2 - 12x + 9 = 4x + 5

To solve for x, we need to bring all terms to one side of the equation. Subtract 4x and 5 from both sides:

4x^2 - 12x + 9 - 4x - 5 = 0

Simplify: 4x^2 - 16x + 4 = 0

Now we have a quadratic equation in the form ax^2 + bx + c = 0. We can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = 4, b = -16, and c = 4. Substitute these values into the quadratic formula:

x = (16 ± √((-16)^2 - 4 * 4 * 4)) / (2 * 4) x = (16 ± √(256 - 64)) / 8 x = (16 ± √192) / 8 x = (16 ± 8√3) / 8

Finally, we can simplify the solutions by dividing both numerator and denominator by 8:

x = 2 ± √3

Therefore, the solutions to the equation (2x-3)^2 = 4x + 5 are x = 2 + √3 and x = 2 - √3.