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=1.03
x equals 1.03

x=−0.89
x equals negative 0.89

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 \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 2\), \(b = -5\), and \(c = -6\).

First, we calculate the discriminant:

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

Now we use the quadratic formula:

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

Calculating \(\sqrt{73}\) gives approximately 8.54. Now we can substitute that back into the formula:

1. For \(x = \frac{5 + \sqrt{73}}{4}\):

\[ x \approx \frac{5 + 8.54}{4} \approx \frac{13.54}{4} \approx 3.385 \]

2. For \(x = \frac{5 - \sqrt{73}}{4}\):

\[ x \approx \frac{5 - 8.54}{4} \approx \frac{-3.54}{4} \approx -0.885 \]

Rounding this to the nearest hundredth gives us:

\[ x \approx -0.89 \]

Thus, the solution is:

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

So, the correct response is:

x = -0.89