How do you solve the equation x2+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=+52 or 52.

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 x2+4x21=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 22=4, so you get the equation that you stated.

This may be re-written as (x+2)2=25.

So x+2=±5.

So x3 or 7.