(x-4)(x+4)-(x+6)^2=-16

2 min read Jun 17, 2024

Solving the Equation: (x-4)(x+4)-(x+6)^2=-16

This article will guide you through the steps to solve the equation (x-4)(x+4)-(x+6)^2=-16. We will use algebraic manipulations to simplify the equation and find the solution(s) for x.

Step 1: Expand the expressions

First, let's expand the products and squares in the equation:

(x-4)(x+4): This is a difference of squares pattern, which expands to x² - 16.
(x+6)²: This expands to x² + 12x + 36.

Substituting these expansions into the original equation, we get:

x² - 16 - (x² + 12x + 36) = -16

Step 2: Simplify the equation

Now we can simplify the equation by removing parentheses and combining like terms:

x² - 16 - x² - 12x - 36 = -16 -12x - 52 = -16

Step 3: Isolate the variable

To isolate x, we'll add 52 to both sides of the equation:

-12x = 36

Step 4: Solve for x

Finally, divide both sides by -12 to find the value of x:

x = -3

Conclusion

Therefore, the solution to the equation (x-4)(x+4)-(x+6)²=-16 is x = -3.