How do you solve using the completing the square method #x^2-20x=10#?

Question

1670 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-06T18:54:47

#x=+-sqrt110-10#

The first step required to complete the square is to have your constant on one side, and variables on the other, in the form

#ax^2+bx=c#. This is the case here.

Now, you must add #(b/2)^2# to each side. Here, #b=-20, (b/2)^2=(-20/2)^2=100#

Thus, we have

#x^2-20x+100=10+100#

#x^2+20x+100=110#

We need to factor the left side. Recognize that #(x^2+20x+100)=(x+10)(x+10)=(x+10)^2#

#(x+10)^2=110#

To solve, take the root of each side, accounting for positive and negative answers.

#sqrt((x+10)^2)=+-sqrt110#

#x+10=+-sqrt110#

Solve.

#x=+-sqrt110-10#