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=−1.03
x equals negative 1.03

x=1.03
x equals 1.03

x=0.89
x equals 0.89

x=−0.89

Answer 1

To solve the quadratic equation \( 2x^2 - 5x - 6 = 0 \), we can use the quadratic formula:

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

In this equation:

• \( a = 2 \)
• \( b = -5 \)
• \( c = -6 \)

Now, plug these values into the formula.

1. Calculate the discriminant \( b^2 - 4ac \):

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

2. Now substitute back into the quadratic formula:

\[ x = \frac{{5 \pm \sqrt{73}}}{4} \]

3. Calculate \( \sqrt{73} \) which is approximately \( 8.54 \).

4. Now calculate the two potential solutions:

\[ x_1 = \frac{{5 + 8.54}}{4} \approx \frac{{13.54}}{4} \approx 3.385 \]

\[ x_2 = \frac{{5 - 8.54}}{4} \approx \frac{{-3.54}}{4} \approx -0.885 \]

Rounding \(-0.885\) to the nearest hundredth gives \(-0.89\).

Thus, the solution to the quadratic equation \( 2x^2 - 5x - 6 = 0 \) that matches one of the provided options is:

x = -0.89.