# How do you solve the equation x^2+4x+4=25 by completing the square?

Dec 29, 2016

$3$ or $- 7$. Re-write the LHS as ${\left(x + 2\right)}^{2}$ then take the square root of both sides. That tells you that $x = + 5 - 2$ or $- 5 - 2$.

#### Explanation:

The way the question is set out half-does the problem for you, as "the square is completed" already. If the question had been "solve ${x}^{2} + 4 x - 21 = 0$, you would have taken the $21$ to the RHS, then added the square of half the number in front of the $x$ to both sides (called "completing the square').. In this case, the number in front of the $x$ is $4$, half it is $2$, square it is ${2}^{2} = 4$, so you get the equation that you stated.

This may be re-written as ${\left(x + 2\right)}^{2} = 25$.

So $x + 2 = \pm 5$.

So $x 3$ or $- 7$.