### Home > CCA2 > Chapter C > Lesson C.1.1 > ProblemC-10

C-10.

Find the real solutions to the equations below using any method of your choice.

1. $2x^2=2−3x$

Rewrite the equation in standard form.
$2x^2+3x=2−3x+3x$
$2x^2+3x=2$
$2x^2+3x−2=2−2$
$2x^2+3x−2=0$

Solve by Zero Product Property:

Factor the equation:
$2x^2+3x−2=0$
$(2x−1)(x+2)=0$

Get the roots from the factors.
$(2x−1)=0$
$x=0.5$

$(x+2)=0$
$x=−2$

In the quadratic formula, substitute the coefficient of $x^2$ for $a$, the coefficient of $x$ for $b$, and the third term for $c$.

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

$x = \frac {-3\; \pm\; \sqrt {3^2\; -\; 4(2)(-2)}}{2(2)}$

Simplify.

$\textit{x}\; =\; \frac {-3\; \pm\; \sqrt {9\; +\; 16}}{4}$

$x = \frac {-3\; \pm\; \sqrt{25}}{4}$

$x = \frac {-3\; \pm\; 5}{4}$

$x=\left\{\frac{2}{4},-\frac{8}{4}\right\}$

$\textit{x}=\frac{1}{2}, -2$

2. $(2x−3)^2+4=0$

See the help for part (a).

This quadratic is not factorable. What happens when you use the other two methods? Are there any real solutions?