To solve the quadratic equation \( 3x^2 + 18x + 24 = 0 \) using the quadratic formula, we start by identifying the coefficients in the standard form of a quadratic equation \( ax^2 + bx + c = 0 \).
Here, we have:
- \( a = 3 \)
- \( b = 18 \)
- \( c = 24 \)
The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Now we can substitute the values of \( a \), \( b \), and \( c \):
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Calculate the discriminant \( b^2 - 4ac \): \[ b^2 = 18^2 = 324 \] \[ 4ac = 4 \times 3 \times 24 = 288 \] \[ b^2 - 4ac = 324 - 288 = 36 \]
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Now substitute into the quadratic formula: \[ x = \frac{-18 \pm \sqrt{36}}{2 \times 3} \] \[ \sqrt{36} = 6 \] \[ x = \frac{-18 \pm 6}{6} \]
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This gives us two solutions:
- First solution: \[ x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2 \]
- Second solution: \[ x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4 \]
Thus, the solutions to the equation \( 3x^2 + 18x + 24 = 0 \) are: \[ x = -2 \quad \text{and} \quad x = -4 \]
Therefore, the correct response is: x = -2, x = -4.