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

1 Answer
Audree
Jul 27, 2016

x=1.79 , x=-2.79

Explanation:

First, we need to get all the terms of the equations on one side of the equation
I added x to the left side
x+x^2=5
then I subtracted 5
-5+x+x^2=0
now I will rearrange the equation to make it look similar to ax^2+bx+c=0
x^2+x-5=0

So we want to use the quadratic formula to find what the roots of x are
the quadratic formula is
x=(-b+-sqrt(b^2-4ac))/(2*a)

from the equation we will identify what a, b, and c are
a=1
b=1
c=-5

now we plug all this in to the formula
x=(-(1)+-sqrt((1)^2-4(1)(-5)))/(2*(1))

next we simplify
x=(-(1)+-sqrt(1+20))/(2)

x=(-1+-sqrt(21))/(2)

x=(-1+-4.58)/(2)

there will be two answers for x because of the +-
x=(-1+4.58)/(2)=3.58/2=1.79
x=(-1-4.58)/(2)=-5.58/2=-2.79

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