(x%2B7)%3D81.jpeg "(x+7)(x+7)=81")
Solving the Equation: (x+7)(x+7) = 81
This equation presents a quadratic expression, and we can solve it by following these steps:
1. Expand the Left Side
First, we expand the left side of the equation using the FOIL method (First, Outer, Inner, Last):
(x + 7)(x + 7) = x² + 7x + 7x + 49
Simplifying, we get:
x² + 14x + 49 = 81
2. Rearrange into Standard Quadratic Form
To solve the quadratic equation, we need to set it equal to zero. Subtract 81 from both sides:
x² + 14x - 32 = 0
3. Solve the Quadratic Equation
Now we have a standard quadratic equation in the form ax² + bx + c = 0. We can solve it using different methods, such as:
- Factoring: In this case, we can factor the quadratic equation as (x + 16)(x - 2) = 0.
- Quadratic Formula: The quadratic formula solves for x in any quadratic equation: x = (-b ± √(b² - 4ac)) / 2a In our equation, a = 1, b = 14, and c = -32. Substitute these values into the formula and solve.
4. Find the Solutions
Using either factoring or the quadratic formula, we find the solutions for x:
- x = -16
- x = 2
Therefore, the solutions to the equation (x + 7)(x + 7) = 81 are x = -16 and x = 2.