(x%2B6)%3D288.jpeg "(x-6)(x+6)=288")
Solving the Equation (x-6)(x+6) = 288
This equation presents a quadratic equation in a slightly disguised form. Let's break down how to solve it:
Expanding the Equation
First, we need to expand the left side of the equation using the distributive property (or the FOIL method):
(x - 6)(x + 6) = x² - 6x + 6x - 36
Simplifying, we get:
x² - 36 = 288
Rearranging and Solving
Now, we have a standard quadratic equation:
x² - 36 - 288 = 0 x² - 324 = 0
We can now solve for x using the square root property:
x² = 324 x = ±√324
Therefore, the solutions are:
x = 18 and x = -18
Verification
We can verify our solutions by substituting them back into the original equation:
- For x = 18: (18 - 6)(18 + 6) = 12 * 24 = 288
- For x = -18: (-18 - 6)(-18 + 6) = -24 * -12 = 288
Both solutions satisfy the original equation, confirming their validity.
Conclusion
By expanding the equation, rearranging terms, and utilizing the square root property, we successfully solved the quadratic equation (x - 6)(x + 6) = 288, obtaining the solutions x = 18 and x = -18.