(x-12)(x+12)=2(x-6)^2-x^2

2 min read Jun 17, 2024

Solving the Equation: (x-12)(x+12) = 2(x-6)^2 - x^2

This article will guide you through the steps to solve the equation (x-12)(x+12) = 2(x-6)^2 - x^2.

Let's begin by expanding both sides of the equation to simplify it:

Left Side: (x-12)(x+12) = x² - 144 (using the difference of squares formula)
Right Side: 2(x-6)² - x² = 2(x² - 12x + 36) - x² = x² - 24x + 72

Now our equation looks like this: x² - 144 = x² - 24x + 72

Notice that we have x² terms on both sides. Subtracting x² from both sides simplifies the equation:

Next, we need to isolate the 'x' term. Let's move the constant terms to one side:

Finally, divide both sides by -24 to solve for x:

Therefore, the solution to the equation (x-12)(x+12) = 2(x-6)² - x² is x = 9.