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:
1. Expanding the Equation
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
2. Rearranging the Equation
To solve for x, we need to set the equation equal to zero:
x² + 10x + 25  49 = 0
Simplifying:
x² + 10x  24 = 0
3. Solving the Quadratic Equation
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.
4. Solutions
Therefore, the solutions to the equation (x+5)(x+5) = 49 are:
x = 12 or x = 2