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=1.03
x equals 1.03

x=−0.89
x equals negative 0.89

x=0.89
x equals 0.89

x=−1.03
x equals negative 1.03

Answer 1

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

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

Next, we can use the quadratic formula to find the solutions, which is given by:

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

In this equation, \( a = 2 \), \( b = -5 \), and \( c = -6 \). Plugging these values into the formula:

1. Calculate the discriminant:

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

2. Now substitute back into the quadratic formula:

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

3. Calculate \( \sqrt{73} \):

\[ \sqrt{73} \approx 8.544 \]

4. Now calculate the two possible values for \( x \):

\[ x_1 = \frac{5 + 8.544}{4} \approx \frac{13.544}{4} \approx 3.386 \]

\[ x_2 = \frac{5 - 8.544}{4} \approx \frac{-3.544}{4} \approx -0.886 \]

Now rounding \( -0.886 \) to the nearest hundredth gives us \( -0.89 \).

The solutions to the equation \( 2x^2 - 5x - 6 = 0 \) include:

1. \( x \approx 3.39 \)
2. \( x \approx -0.89 \)

From the given options, the solution that corresponds to the quadratic equation is:

x = −0.89.