How do you solve #x^2+2x=9# by completing the square?

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Answer 1 · 2017-03-12T07:40:11

The solutions are #S={-4.162, 2.162}#

Let's complete the square

#x^2+2x=9#

We add #(2/2)^2# to both sides

#x^2+2x+1=9+1#

The #LHS# is

#(a^2+2ab+b^2)=(a+b)^2#

#(x+1)^2=10#

Taking square roots on both sides

#x+1=+-sqrt10#

#x=-1+-sqrt10#

#x_1=-1-sqrt10=-4.162#

#x_2=-1+sqrt10=2.162#