# How do you use the quadratic formula to solve -x^2+1=-5x^2+4x?

Feb 17, 2017

Move all the terms to one side of the equation, then plug it in.

#### Explanation:

To start, move all the terms to one side so on one side of the equation, there is only a 0. You would end up with $4 {x}^{2} - 4 x + 1 = 0$
From that, you can get that A is equal to 4, B is equal to -4, and C is equal to 1. Plug that into the quadratic equation, which is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 \left(a\right) \left(c\right)}}{2 a}$
After plugging it in, you get $x = \frac{- \left(- 4\right) \pm \sqrt{{\left(- 4\right)}^{2} - 4 \left(4\right) \left(1\right)}}{2 \left(4\right)}$
Simplify and you'll get $x = \frac{4 \pm \sqrt{0}}{8}$
Keep simplifying and you'll end up with $\frac{1}{2}$
And that is the value of X.

But there is an easier way. You can factor $4 {x}^{2} - 4 x + 1 = 0$ into ${\left(2 x - 1\right)}^{2} = 0$
Since that is equal to 0, one of the factors must be equal to 0 and since the factors are equal, then there is only one answer. Set $2 x - 1$ equal to 0 and solve for X to get $\frac{1}{2}$.