What is the solution to the equation x^2 + 2x - 8 = 0?

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Question: What is the solution to the equation x^2 + 2x - 8 = 0?

Options:

Correct Answer: x = 4, -2

Solution:

Factoring gives (x + 4)(x - 2) = 0. Thus, x = -4 or x = 2.

What is the solution to the equation x^2 + 2x - 8 = 0?

What is the solution to the equation x^2 + 2x - 8 = 0?

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 4 and -2 work because 4 * -2 = -8 and 4 + (-2) = 2.
Step 4: Rewrite the equation using these numbers: (x + 4)(x - 2) = 0.
Step 5: Set each factor equal to zero: x + 4 = 0 and x - 2 = 0.
Step 6: Solve the first equation: x + 4 = 0 gives x = -4.
Step 7: Solve the second equation: x - 2 = 0 gives x = 2.
Step 8: The solutions are x = -4 and x = 2.

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