Solve the equation 2x^2 + 4x - 6 = 0.

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Question: Solve the equation 2x^2 + 4x - 6 = 0.

Options:

Correct Answer: x = 1, -3

Solution:

First, divide the equation by 2: x^2 + 2x - 3 = 0. Factor to (x + 3)(x - 1) = 0. Thus, x = -3 and x = 1.

Solve the equation 2x^2 + 4x - 6 = 0.

Solve the equation 2x^2 + 4x - 6 = 0.

Step 1: Start with the equation 2x^2 + 4x - 6 = 0.
Step 2: Divide every term in the equation by 2 to simplify it. This gives you x^2 + 2x - 3 = 0.
Step 3: Now, we need to factor the quadratic equation x^2 + 2x - 3.
Step 4: Look for two numbers that multiply to -3 (the constant term) and add to 2 (the coefficient of x). These numbers are 3 and -1.
Step 5: Write the factored form of the equation using these numbers: (x + 3)(x - 1) = 0.
Step 6: Set each factor equal to zero: x + 3 = 0 and x - 1 = 0.
Step 7: Solve for x in each equation. From x + 3 = 0, we get x = -3. From x - 1 = 0, we get x = 1.
Step 8: The solutions to the equation are x = -3 and x = 1.

Quadratic Equations – Understanding how to solve quadratic equations using factoring and the quadratic formula.
Factoring – Recognizing how to factor quadratic expressions to find their roots.
Simplification – The importance of simplifying equations before solving them.