Find the value of x in the equation 3x^2 + 12x + 12 = 0.

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Question: Find the value of x in the equation 3x^2 + 12x + 12 = 0.

Options:

Correct Answer: -4

Solution:

Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0. Factoring gives (x + 2)(x + 2) = 0, so x = -2.

Find the value of x in the equation 3x^2 + 12x + 12 = 0.

Find the value of x in the equation 3x^2 + 12x + 12 = 0.

Step 1: Start with the equation 3x^2 + 12x + 12 = 0.
Step 2: Divide every term in the equation by 3 to simplify it. This gives you x^2 + 4x + 4 = 0.
Step 3: Now, look for two numbers that multiply to 4 (the last number) and add up to 4 (the middle number). These numbers are 2 and 2.
Step 4: Rewrite the equation using these numbers: (x + 2)(x + 2) = 0.
Step 5: Since (x + 2)(x + 2) = 0, you can set x + 2 = 0.
Step 6: Solve for x by subtracting 2 from both sides: x = -2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring and the quadratic formula.
Factoring – Recognizing how to factor a quadratic expression into binomials.
Simplifying Equations – The importance of simplifying equations before solving.