Question

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

Answer 1

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 `4x^2-4x+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=(-b+-sqrt(b^2-4(a)(c)))/(2a)`
After plugging it in, you get `x=(-(-4)+-sqrt((-4)^2-4(4)(1)))/(2(4))`
Simplify and you'll get `x=(4+-sqrt(0))/8`
Keep simplifying and you'll end up with `1/2`
And that is the value of X.

But there is an easier way. You can factor `4x^2-4x+1=0` into `(2x-1)^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 `2x-1` equal to 0 and solve for X to get `1/2`.