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What are the solutions to the equation x^2 + 2x - 8 = 0?
What are the solutions to the equation x^2 + 2x - 8 = 0?
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Practice Questions
1 question
Q1
What are the solutions to the equation x^2 + 2x - 8 = 0?
x = 2, -4
x = -2, 4
x = 4, -2
x = -4, 2
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Factoring gives (x + 4)(x - 2) = 0, so x = -4 and x = 2.
Questions & Step-by-step Solutions
1 item
Q
Q: What are the solutions to the equation x^2 + 2x - 8 = 0?
Solution:
Factoring gives (x + 4)(x - 2) = 0, so x = -4 and x = 2.
Steps: 10
Show Steps
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.
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