To solve the quadratic equation \(2x^2 + 7x - 15 = 0\) using the quadratic formula, we can identify the coefficients as follows:
- \(a = 2\)
- \(b = 7\)
- \(c = -15\)
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Plugging in the coefficients:
- Calculate \(b^2\):
\[ b^2 = 7^2 = 49 \]
- Calculate \(4ac\):
\[ 4ac = 4 \cdot 2 \cdot (-15) = -120 \]
- Now, calculate \(b^2 - 4ac\):
\[ b^2 - 4ac = 49 - (-120) = 49 + 120 = 169 \]
Now, substituting this back into the quadratic formula:
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
Now, we find \(\sqrt{169}\):
\[ \sqrt{169} = 13 \]
Thus, we have:
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the value that goes in place of ??? is \(13\).
So the complete answer is:
13
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