How do you use the quadratic formula to solve -x^2+1=-5x^2+4x−x2+1=−5x2+4x?

1 Answer
arzhao
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 4x^2-4x+1=04x2−4x+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)x=−b±√b2−4(a)(c)2a
After plugging it in, you get x=(-(-4)+-sqrt((-4)^2-4(4)(1)))/(2(4))x=−(−4)±√(−4)2−4(4)(1)2(4)
Simplify and you'll get x=(4+-sqrt(0))/8x=4±√08
Keep simplifying and you'll end up with 1/212
And that is the value of X.

But there is an easier way. You can factor 4x^2-4x+1=04x2−4x+1=0 into (2x-1)^2=0(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-12x−1 equal to 0 and solve for X to get 1/212.

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