Suppose you are a solving a quadratic equation using the quadratic formula and this is your work so far:

To solve the quadratic equation \(2x^2 + 7x - 15 = 0\) using the quadratic formula, we first identify the coefficients:

• \(a = 2\)
• \(b = 7\)
• \(c = -15\)

The quadratic formula is given by:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Now, we need to calculate the discriminant, \(b^2 - 4ac\):

1. Calculate \(b^2\): \[ b^2 = 7^2 = 49 \]

2. Calculate \(4ac\): \[ 4ac = 4 \cdot 2 \cdot (-15) = 8 \cdot (-15) = -120 \]

3. Now calculate the discriminant \(b^2 - 4ac\): \[ b^2 - 4ac = 49 - (-120) = 49 + 120 = 169 \]

Now, we substitute this back into the quadratic formula:

\[ x = \frac{-7 \pm \sqrt{169}}{4} \]

The square root of 169 is 13. Thus, we can replace ??? with 13, so it would look like this:

\[ x = \frac{-7 \pm 13}{4} \]

Therefore, the value that goes in place of ??? is 13.

Yes, I'm confident in the calculation, but let's confirm the steps to ensure everything is clear.

Given the quadratic equation:

\[ 2x^2 + 7x - 15 = 0 \]

We identify the coefficients:

• \(a = 2\)
• \(b = 7\)
• \(c = -15\)

Now we apply the quadratic formula, which is:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Step 1: Calculate \(b^2 - 4ac\)

1. Calculate \(b^2\): \[ b^2 = 7^2 = 49 \]

2. Calculate \(4ac\): \[ 4ac = 4 \cdot 2 \cdot (-15) = 8 \cdot (-15) = -120 \]

3. Calculate the discriminant: \[ b^2 - 4ac = 49 - (-120) = 49 + 120 = 169 \]

Step 2: Substitute into the formula

Now we substitute the values back into the quadratic formula:

\[ x = \frac{-7 \pm \sqrt{169}}{2 \times 2} \]

The square root of 169 is 13:

\[ x = \frac{-7 \pm 13}{4} \]

Thus, the number that goes in place of ??? is indeed 13.

Let me know if you have any further questions!