Question

Use the quadratic equation x = -b ± with the square root of b^2 -4ac/ 2a, to solve 2x^2 + 7x - 15= 0

Answer 1

To solve the quadratic equation \(2x^2 + 7x - 15 = 0\) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\) from the equation, which is in the form \(ax^2 + bx + c = 0\):

- \(a = 2\)
- \(b = 7\)
- \(c = -15\)

The quadratic formula is given by:

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

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

\[
b^2 = 7^2 = 49
\]
\[
4ac = 4 \times 2 \times (-15) = -120
\]
\[
b^2 - 4ac = 49 - (-120) = 49 + 120 = 169
\]

Now substitute the values of \(a\), \(b\), and the discriminant into the quadratic formula:

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

Calculating the square root:

\[
\sqrt{169} = 13
\]

Now we can plug that back into the formula:

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

This results in two possible solutions:

1. Using \(+\):
\[
x = \frac{-7 + 13}{4} = \frac{6}{4} = \frac{3}{2}
\]

2. Using \(-\):
\[
x = \frac{-7 - 13}{4} = \frac{-20}{4} = -5
\]

Thus, the solutions to the equation \(2x^2 + 7x - 15 = 0\) are:

\[
x = \frac{3}{2} \quad \text{and} \quad x = -5
\]