(x+1)^2-9=0

Jasonbradley

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Jun 16, 2024

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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.