Factor out 4x: 4x(x + 2) = 0. Thus, x = 0 or x + 2 = 0 gives x = -2.
Solve for x: 4x^2 + 8x = 0.
Practice Questions
Q1
Solve for x: 4x^2 + 8x = 0.
x = 0, -2
x = 2, -2
x = 0, 2
x = -4, 0
Questions & Step-by-Step Solutions
Solve for x: 4x^2 + 8x = 0.
Step 1: Start with the equation 4x^2 + 8x = 0.
Step 2: Look for a common factor in both terms. Here, the common factor is 4x.
Step 3: Factor out 4x from the equation. This gives you 4x(x + 2) = 0.
Step 4: Set each factor equal to zero. First, set 4x = 0.
Step 5: Solve 4x = 0 by dividing both sides by 4. This gives x = 0.
Step 6: Now set the second factor x + 2 = 0.
Step 7: Solve x + 2 = 0 by subtracting 2 from both sides. This gives x = -2.
Step 8: The solutions are x = 0 and x = -2.
Factoring Quadratic Equations – The question tests the ability to factor a quadratic equation and solve for its roots.
Zero Product Property – The question assesses 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.
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