Answer
$x = 0.13~~$ or $~~x = 3.87$
Work Step by Step
A quadratic equation can be written in this form:
$ax^2 + bx+c = 0$
where $a,b,$ and $c$ are real numbers and $a \neq 0$
We can determine the values of $a, b,$ and $c$:
$2x^2 = 8x-1$
$2x^2 -8x+1 = 0$
$a = 2$
$b = -8$
$c = 1$
We can use the quadratic formula to find the solutions of the equation:
$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$x = \frac{-(-8) \pm \sqrt{(-8)^2-(4)(2)(1)}}{(2)(2)}$
$x = \frac{8 \pm \sqrt{64-8}}{4}$
$x = \frac{8 \pm \sqrt{56}}{4}$
$x = \frac{8 - \sqrt{56}}{4}~~$ or $~~x = \frac{8 + \sqrt{56}}{4}$
$x = 0.13~~$ or $~~x = 3.87$
