Answer
$B$
Work Step by Step
First, we want to simplify this equation by dividing all terms by their greatest common factor, $3$:
$2x^2 + 3x - 5 = 0$
We need to find which factors multiplied together will equal $ac$ but when added together will equal $b$. The $a$ is the coefficient of the first term, $b$ is the coefficient of the second term, and $c$ is the constant term.
In this equation, $ac$ is $-10$ and $b$ is $3$. By looking at the equation, we can see that we need one positive factor and one negative factor, with the positive factor having the greater absolute value. Let's look at the possibilities:
$5$ and $-2$
$10$ and $-1$
It looks like the first option will work.
Let's rewrite the equation and split the middle term using these two factors:
$2x^2 + 5x - 2x - 5 = 0$
Group the first two and last two terms:
$(2x^2 + 5x) - (2x + 5) = 0$
Factor common terms out:
$x(2x + 5) - (2x + 5) = 0$
Group the factors:
$(2x + 5)(x - 1) = 0$
Set the first factor equal to $0$:
$2x + 5 = 0$
Subtract $5$ from each side of the equation:
$2x = -5$
Divide each side by $2$:
$x = -\frac{5}{2}$
Set the second factor equal to $0$:
$x - 1 = 0$
Add $1$ to each side to solve for $x$:
$x = 1$
The solution to this equation is $x = -\frac{5}{2}$ or $x = 1$.
This corresponds with answer option $B$.
