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

1 Answer
Dec 29, 2016

3 or -7. Re-write the LHS as (x+2)^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+4x-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 (x+2)^2=25.

So x+2 = +-5.

So x 3 or -7.