Solve for x: x^2 + 2x - 8 = 0.

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Question: Solve for x: x^2 + 2x - 8 = 0.

Options:

Correct Answer: x = 4, -2

Solution:

Factoring gives (x + 4)(x - 2) = 0. Thus, the solutions are x = -4 and x = 2.

Solve for x: x^2 + 2x - 8 = 0.

Solve for x: 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 constant term) and add to 2 (the coefficient of x).
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 for x in each equation: For x + 4 = 0, x = -4; for x - 2 = 0, x = 2.
Step 7: The solutions 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 question tests understanding of the zero product property, which states that if the product of two factors is zero, at least one of the factors must be zero.