Question

Which of the following is a solution to the quadratic equation 2x^2−5x=6? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)
Responses

x=0.89

x=−0.89

x=1.03

x=−1.03

Answer 1

To solve the quadratic equation \(2x^2 - 5x = 6\), we first rearrange it into standard form:

\[
2x^2 - 5x - 6 = 0
\]

Next, we can use the quadratic formula, which is given by:

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

In our equation, the coefficients are:
- \(a = 2\)
- \(b = -5\)
- \(c = -6\)

Now we plug these values into the quadratic formula:

1. Calculate the discriminant \(b^2 - 4ac\):

\[
b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73
\]

2. Now, substituting back into the formula:

\[
x = \frac{5 \pm \sqrt{73}}{4}
\]

3. Calculate \(\sqrt{73}\):

\(\sqrt{73} \approx 8.54\) (to two decimal places)

4. Substitute back into the equation:

\[
x = \frac{5 \pm 8.54}{4}
\]

Calculating the two possible values for \(x\):

- **For the plus sign**:

\[
x = \frac{5 + 8.54}{4} = \frac{13.54}{4} \approx 3.39
\]

- **For the minus sign**:

\[
x = \frac{5 - 8.54}{4} = \frac{-3.54}{4} \approx -0.89
\]

So the two solutions rounded to the nearest hundredth are approximately \(x \approx 3.39\) and \(x \approx -0.89\).

From the given options, the solution that matches our calculation is:

\(\boxed{-0.89}\)