Which of the following is a solution to the quadratic equation 2x2−5x=6 ? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)

Question

Responses

x=0.89
x equals 0.89

x=−0.89
x equals negative 0.89

x=1.03
x equals 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 apply the quadratic formula:

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

In this case, \( a = 2 \), \( b = -5 \), and \( c = -6 \).

First, we calculate the discriminant:

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

Now, we substitute back into the quadratic formula:

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

Calculating the two possible values:

1. \( x = \frac{5 + \sqrt{73}}{4} \)
2. \( x = \frac{5 - \sqrt{73}}{4} \)

Now, we will compute the approximate values of these expressions. The approximate value of \( \sqrt{73} \) is about 8.544.

1. For \( x = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386 \)
2. For \( x = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886 \)

Now rounding to the nearest hundredth, we have:

• \( 3.39 \) for the first solution
• \( -0.89 \) for the second solution

Thus, the correct rounded solution to the quadratic equation \( 2x^2 - 5x = 6 \) is:

x = -0.89.