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

1 Answer
Feb 17, 2017

Answer:

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#.