Question

Completing the Square & the Quadratic Formula Quick Check
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Question
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)
Responses

x=−0.89
x equals negative 0.89

x=−1.03
x equals negative 1.03

x=0.89
x equals 0.89

x=1.03
x equals 1.03

Answer 1

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

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

Next, we can use the quadratic formula:

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

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

Let's calculate the discriminant (\(b^2 - 4ac\)):

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

Now we can substitute \(a\), \(b\), and the discriminant into the quadratic formula:

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

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

1. For \(x_1 = \frac{5 + \sqrt{73}}{4}\)
2. For \(x_2 = \frac{5 - \sqrt{73}}{4}\)

Calculating these values:

1. Approximately,
\[
\sqrt{73} \approx 8.544
\]
Thus,
\[
x_1 = \frac{5 + 8.544}{4} \approx \frac{13.544}{4} \approx 3.386
\]

2. Then,
\[
x_2 = \frac{5 - 8.544}{4} \approx \frac{-3.544}{4} \approx -0.886
\]

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

Thus, the solution to the equation **rounded to the nearest hundredth** is:

**\(x \approx -0.89\)**

So the correct answer is:

**x = -0.89**