%5E2-9%3D0.jpeg "(x+1)^2-9=0")
Solving the Equation (x+1)^2 - 9 = 0
This equation is a quadratic equation in disguise. We can solve it by following these steps:
1. Simplifying the Equation
- Expand the square: (x+1)^2 = x^2 + 2x + 1
- Substitute: The equation becomes: x^2 + 2x + 1 - 9 = 0
- Combine constants: x^2 + 2x - 8 = 0
2. Solving the Quadratic Equation
Now we have a standard quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = 2, and c = -8. We can solve this using various methods:
a) Factoring:
- Find two numbers that add up to b (2) and multiply to c (-8). These numbers are 4 and -2.
- Factor the equation: (x + 4)(x - 2) = 0
- Set each factor to zero and solve for x:
- x + 4 = 0 => x = -4
- x - 2 = 0 => x = 2
b) Quadratic Formula:
- The quadratic formula solves for x in any equation of the form ax^2 + bx + c = 0:
- x = (-b ± √(b^2 - 4ac)) / 2a
- Substitute the values:
- x = (-2 ± √(2^2 - 4 * 1 * -8)) / 2 * 1
- x = (-2 ± √(36)) / 2
- x = (-2 ± 6) / 2
- Solve for x:
- x = (-2 + 6) / 2 = 2
- x = (-2 - 6) / 2 = -4
3. Solution
Therefore, the solutions to the equation (x+1)^2 - 9 = 0 are x = 2 and x = -4.