which of the following is a solution to the quadratic equation 2x^2 - 5x = 6 assume that the solution has been rounded to the nearest hunderdth, if applicable

Answer 1

To find the solutions to the quadratic equation $2x^2-5x=6$, we first rewrite it in standard form:

$$2x^2-5x-6=0$$

Next, we can use the quadratic formula:

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

where $a=2$, $b=-5$, and $c=-6$.

We'll first calculate the discriminant ($b^2-4ac$):

$$b^2-4ac=(-5{)}^2-4(2)(-6)$$ $$=25+48=73$$

Now, substituting the values into the quadratic formula:

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

Now we will calculate the two potential solutions:

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

We will approximate $\sqrt{73}$:

$\sqrt{73}\approx 8.544$

Calculating $x_1$:

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

Calculating $x_2$:

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

Thus, the solutions to the equation $2x^2-5x-6=0$ approximate to:

• $x_1\approx 3.39$ (rounded to the nearest hundredth)
• $x_2\approx -0.89$ (rounded to the nearest hundredth)

So, the solutions are approximately $3.39$ and $-0.89$.