Jasonbradley
Home

(x+5)(x-5)=(x-3)2-16

2 min read Jun 17, 2024
(x+5)(x-5)=(x-3)2-16

Solving the Equation (x+5)(x-5) = (x-3)2 - 16

This article will guide you through the steps of solving the equation (x+5)(x-5) = (x-3)2 - 16. We will use algebraic manipulation to simplify the equation and find the value(s) of x that satisfy it.

Expanding and Simplifying Both Sides

  1. Expand the left side: The left side of the equation is in the form of the "difference of squares" pattern: (a+b)(a-b) = a² - b². Therefore, we can expand it as follows: (x+5)(x-5) = x² - 5² = x² - 25

  2. Expand the right side: The right side involves squaring a binomial. We can use the formula (a-b)² = a² - 2ab + b² to expand it: (x-3)² - 16 = x² - 2(x)(3) + 3² - 16 = x² - 6x + 9 - 16 = x² - 6x - 7

Solving the Quadratic Equation

Now we have: x² - 25 = x² - 6x - 7

  1. Simplify by subtracting x² from both sides: -25 = -6x - 7

  2. Add 7 to both sides: -18 = -6x

  3. Divide both sides by -6: x = 3

Conclusion

Therefore, the solution to the equation (x+5)(x-5) = (x-3)² - 16 is x = 3.

Related Post

Featured Posts