Solve for x: 5x^2 + 10x = 0.

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Question: Solve for x: 5x^2 + 10x = 0.

Options:

Correct Answer: x = 0, -2

Solution:

Factoring gives 5x(x + 2) = 0, so x = 0 or x = -2.

Solve for x: 5x^2 + 10x = 0.

Solve for x: 5x^2 + 10x = 0.

Correct Answer: x = 0 or x = -2

Step 1: Start with the equation 5x^2 + 10x = 0.
Step 2: Factor out the common term from both parts of the equation. The common term is 5x.
Step 3: Rewrite the equation as 5x(x + 2) = 0.
Step 4: Set each factor equal to zero. First, set 5x = 0.
Step 5: Solve for x in the first factor: 5x = 0 means x = 0.
Step 6: Now set the second factor equal to zero: x + 2 = 0.
Step 7: Solve for x in the second factor: x + 2 = 0 means x = -2.
Step 8: The solutions are x = 0 and x = -2.

Factoring Quadratic Equations – The process of rewriting a quadratic equation in the form of a product of its factors to find the roots.
Zero Product Property – If the product of two factors equals zero, at least one of the factors must be zero.