(x+5)(x+5)=49

2 min read Jun 16, 2024

Solving the Equation (x+5)(x+5) = 49

This equation presents a straightforward quadratic equation that can be solved using a few simple steps. Let's break it down:

First, we need to expand the left side of the equation by applying the distributive property (or FOIL method):

(x+5)(x+5) = x² + 5x + 5x + 25 = x² + 10x + 25

Now the equation becomes:

x² + 10x + 25 = 49

To solve for x, we need to set the equation equal to zero:

x² + 10x + 25 - 49 = 0

Simplifying:

x² + 10x - 24 = 0

We now have a standard quadratic equation in the form ax² + bx + c = 0. There are several methods to solve this, including:

Factoring: We can try to factor the equation into two binomials. In this case, we find that: (x + 12)(x - 2) = 0 This leads to two possible solutions: x = -12 or x = 2.
Quadratic Formula: The quadratic formula can be used to solve any quadratic equation. It states:

x = (-b ± √(b² - 4ac)) / 2a

Applying this to our equation (where a = 1, b = 10, c = -24):

x = (-10 ± √(10² - 4 * 1 * -24)) / 2 * 1 x = (-10 ± √(196)) / 2 x = (-10 ± 14) / 2

This gives us the solutions: x = -12 or x = 2.

Therefore, the solutions to the equation (x+5)(x+5) = 49 are:

x = -12 or x = 2