Question

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

2x2+7x−15=0



x=
−7 ±72−42−15
22​



x=
−7 ±???
4​👈





What number goes in place of ???

Answer 1

are you sure

Answer 2

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**.

Answer 3

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!