Which of the following is a solution to the quadratic equation 2x2−5x=6

Question

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

x=1.03
x equals 1.03

x=0.89
x equals 0.89

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 to the standard form:

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

Next, we can use the quadratic formula:

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

Here, \(a = 2\), \(b = -5\), and \(c = -6\).

1. Calculate the discriminant: \[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]

2. Now apply the quadratic formula: \[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]

3. Calculate the two possible solutions: \[ x_1 = \frac{5 + \sqrt{73}}{4} \] \[ x_2 = \frac{5 - \sqrt{73}}{4} \]

Calculating \( \sqrt{73} \): \[ \sqrt{73} \approx 8.544 \]

Calculating \(x_1\): \[ x_1 = \frac{5 + 8.544}{4} \approx \frac{13.544}{4} \approx 3.386 \]

Calculating \(x_2\): \[ x_2 = \frac{5 - 8.544}{4} \approx \frac{-3.544}{4} \approx -0.886 \]

Rounding to the nearest hundredth, we get: \[ x_2 \approx -0.89 \]

Thus, the solution to the quadratic equation \(2x^2 - 5x = 6\) that rounds to the nearest hundredth is:

\(x \approx -0.89\)

Therefore, the correct response is: x = −0.89.