Question

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

Answer 1

For `ax^2+bx+c=0`, the quadratic formula is `x=(-b+-sqrt(b^2-4ac))/(2a)`.

Explanation:

First we need to get the equation to standard quadratic form by subtracting 4x from both sides:
`x^2-4x+2x=0` which we can simplify by combining like-terms
`x^2-2x=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=(-b+-sqrt(b^2-4ac))/(2a)`
`x=(-(-2)+-sqrt((-2)^2-4*1*0))/(2*1)`
`x=(2+-sqrt(4))/2`
`x=(2+-2)/2`
`x=(1+-1)/1`
so `x=0` or `x=2`