Question

Completing the Square & the Quadratic Formula Quick Check
4 of 54 of 5 Items
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=1.03
x equals 1.03

x=0.89
x equals 0.89

x=−1.03
x equals negative 1.03

x=−0.89

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 either complete the square or use the quadratic formula. Here, we'll use the quadratic formula:

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

In our equation, \(a = 2\), \(b = -5\), and \(c = -6\).

Now, we calculate the discriminant \(b^2 - 4ac\):

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

Now plug in the values into the quadratic formula:

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

This simplifies to:

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

Now we need to calculate both potential solutions:

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

**Finding the two solutions**:

1. **First solution**:
\[
x_1 = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386
\]

2. **Second solution**:
\[
x_2 = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886
\]

Rounding to the nearest hundredth:

- \(x_1 \approx 3.39\)
- \(x_2 \approx -0.89\)

Thus, among the choices provided:

- x = -0.89 is a solution.

Therefore, the correct response is:

**x = -0.89**.