How do you use the quadratic formula to solve x^2+2x=4x?

May 7, 2017

For $a {x}^{2} + b x + c = 0$, the quadratic formula is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

Explanation:

First we need to get the equation to standard quadratic form by subtracting 4x from both sides:
${x}^{2} - 4 x + 2 x = 0$ which we can simplify by combining like-terms
${x}^{2} - 2 x = 0$
Here we can see that according to the standard quadratic form, a=1, b=-2, and c=0.
By plugging these values into the quadratic formula, $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$x = \frac{- \left(- 2\right) \pm \sqrt{{\left(- 2\right)}^{2} - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$
$x = \frac{2 \pm \sqrt{4}}{2}$
$x = \frac{2 \pm 2}{2}$
$x = \frac{1 \pm 1}{1}$
so $x = 0$ or $x = 2$