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

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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.

$x=+-sqrt110-10$

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