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

Question

4986 views around the world

You can reuse this answer
Creative Commons License

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

$x+1=+-sqrt10$

$x=-1+-sqrt10$

$x_1=-1-sqrt10=-4.162$

$x_2=-1+sqrt10=2.162$

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