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What are the solutions to the equation x^2 + 2x - 8 = 0?

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Question: What are the solutions to the equation x^2 + 2x - 8 = 0?

Options:

  1. x = 2, -4
  2. x = -2, 4
  3. x = 4, -2
  4. x = -4, 2

Correct Answer: x = 4, -2

Solution: 

Factoring gives (x + 4)(x - 2) = 0, so x = -4 and x = 2.

What are the solutions to the equation x^2 + 2x - 8 = 0?

Practice Questions

Q1
What are the solutions to the equation x^2 + 2x - 8 = 0?
  1. x = 2, -4
  2. x = -2, 4
  3. x = 4, -2
  4. x = -4, 2

Questions & Step-by-Step Solutions

What are the solutions to the equation x^2 + 2x - 8 = 0?
Correct Answer: x = -4 and x = 2
  • Step 1: Start with the equation x^2 + 2x - 8 = 0.
  • Step 2: Look for two numbers that multiply to -8 (the last number) and add to 2 (the middle number).
  • Step 3: The numbers that work are 4 and -2 because 4 * -2 = -8 and 4 + (-2) = 2.
  • Step 4: Rewrite the equation using these numbers: x^2 + 4x - 2x - 8 = 0.
  • Step 5: Group the terms: (x^2 + 4x) + (-2x - 8) = 0.
  • Step 6: Factor each group: x(x + 4) - 2(x + 4) = 0.
  • Step 7: Factor out the common term (x + 4): (x + 4)(x - 2) = 0.
  • Step 8: Set each factor equal to zero: x + 4 = 0 or x - 2 = 0.
  • Step 9: Solve for x: From x + 4 = 0, we get x = -4. From x - 2 = 0, we get x = 2.
  • Step 10: The solutions to the equation are x = -4 and x = 2.
  • Quadratic Equations – The question tests the ability to solve a quadratic equation using factoring.
  • Factoring – The solution requires knowledge of how to factor a quadratic expression.
  • Zero Product Property – The application of the zero product property is necessary to find the solutions after factoring.
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