(x+3)(x-3)=27

2 min read Jun 16, 2024

Solving the Equation (x+3)(x-3) = 27

This article will guide you through solving the equation (x+3)(x-3) = 27.

Understanding the Equation

The equation (x+3)(x-3) = 27 involves a product of two binomials. This pattern is a special case in algebra known as the "difference of squares" pattern.

The Difference of Squares Pattern:

(a + b)(a - b) = a² - b²

Solving the Equation

Expand the left side: Using the difference of squares pattern, we can expand the left side of the equation: (x + 3)(x - 3) = x² - 3² (x + 3)(x - 3) = x² - 9
Rewrite the equation: Now our equation becomes: x² - 9 = 27
Isolate the x² term: Add 9 to both sides of the equation: x² = 27 + 9 x² = 36
Solve for x: Take the square root of both sides: x = ±√36 x = ±6

Solutions

Therefore, the solutions to the equation (x+3)(x-3) = 27 are:

x = 6
x = -6

Verification

We can verify these solutions by plugging them back into the original equation:

For x = 6: (6 + 3)(6 - 3) = (9)(3) = 27
For x = -6: (-6 + 3)(-6 - 3) = (-3)(-9) = 27

Both solutions satisfy the original equation.