Which of the following is a solution to the quadratic equation 2x^2−5x=6

Question

? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)
Responses

x=0.89
x equals 0.89

x=1.03
x equals 1.03

x=−1.03
x equals negative 1.03

x=−0.89

Answer 1

To solve the quadratic equation \(2x^2 - 5x - 6 = 0\), we can first rearrange it to the standard form:

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

Next, we will use the quadratic formula, which is

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

For our equation, the coefficients are:

• \(a = 2\)
• \(b = -5\)
• \(c = -6\)

Now we can calculate \(b^2 - 4ac\):

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

Now substituting back into the quadratic formula:

\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]

Now we will calculate the two possible values for \(x\):

1. Using the positive root:

\[ x_1 = \frac{5 + \sqrt{73}}{4} \approx \frac{5 + 8.544}{4} \approx \frac{13.544}{4} \approx 3.386 \]

2. Using the negative root:

\[ x_2 = \frac{5 - \sqrt{73}}{4} \approx \frac{5 - 8.544}{4} \approx \frac{-3.544}{4} \approx -0.886 \]

When rounded to the nearest hundredth, \(x_2 \approx -0.89\).

So, the solution rounded to the nearest hundredth is:

\[ \boxed{x = -0.89} \]

Thus, the correct response from the given options is:

x = −0.89.