(x+7)(x-7)=-3

2 min read Jun 17, 2024

Solving the Equation (x+7)(x-7) = -3

This equation presents a quadratic expression, and we can solve it by following these steps:

First, we expand the product on the left-hand side of the equation using the difference of squares pattern:

(x+7)(x-7) = x² - 7² = x² - 49

This gives us the equation:

x² - 49 = -3

Now, we move the constant term to the left-hand side to set the equation equal to zero:

x² - 49 + 3 = 0

x² - 46 = 0

We now have a simple quadratic equation in the form of ax² + bx + c = 0, where a = 1, b = 0, and c = -46.

There are several ways to solve this equation:

Factoring: In this case, factoring might be difficult, as 46 doesn't have many factors.
Quadratic Formula: The most reliable way is to use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values:

x = (0 ± √(0² - 4 * 1 * -46)) / 2 * 1

x = ± √(184) / 2

x = ± 2√46 / 2

x = ± √46

Therefore, the solutions to the equation (x+7)(x-7) = -3 are:

x = √46 and x = -√46

These are the two values of x that satisfy the original equation.