Question

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

Answer 1

`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`.