Solve the quadratic equation 3x^2 + 12x + 12 = 0.

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Question: Solve the quadratic equation 3x^2 + 12x + 12 = 0.

Options:

Correct Answer: x = -4

Solution:

Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0, which factors to (x + 2)(x + 2) = 0. Thus, x = -2.

Solve the quadratic equation 3x^2 + 12x + 12 = 0.

Solve the quadratic equation 3x^2 + 12x + 12 = 0.

Step 1: Start with the quadratic equation: 3x^2 + 12x + 12 = 0.
Step 2: Divide the entire equation by 3 to simplify it: (3x^2)/3 + (12x)/3 + (12)/3 = 0, which simplifies to x^2 + 4x + 4 = 0.
Step 3: Now, we need to factor the equation x^2 + 4x + 4.
Step 4: Notice that x^2 + 4x + 4 can be written as (x + 2)(x + 2) or (x + 2)^2.
Step 5: Set the factored equation equal to zero: (x + 2)(x + 2) = 0.
Step 6: To find the value of x, set x + 2 = 0.
Step 7: Solve for x by subtracting 2 from both sides: x = -2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, completing the square, or the quadratic formula.
Factoring – Recognizing how to factor a quadratic expression into binomials.
Simplifying Equations – The importance of simplifying equations by dividing by a common factor.