To write the quadratic equation \( 3x^2 + 18x + 24 = 0 \) in the standard form of the quadratic formula, we need to identify the coefficients \( a \), \( b \), and \( c \).
The standard form of a quadratic equation is:
\[ ax^2 + bx + c = 0 \]
For the equation \( 3x^2 + 18x + 24 = 0 \):
- \( a = 3 \)
- \( b = 18 \)
- \( c = 24 \)
So, \( c = 24 \).
Now, we can write the equation in the quadratic formula form, which is
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ x = \frac{-18 \pm \sqrt{18^2 - 4 \cdot 3 \cdot 24}}{2 \cdot 3} \]
This is the quadratic formula applied to the given equation.
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