Question

Solve x^2+2x=4 for x by completing the square

Answer 1

X² + 2x = 4

When completing the square, the goal is to create

a perfect square trinomial on the left side of the equation.

The number used to create one will come from

half the coefficient of the middle term squared.

In this case, that's half of 2 squared or 1 squared, which is 1.

So we add 1 to both sides giving us x² + 2x + 1 = 5.

From here, we set this as a binomial squared.

The first term is an x and the second term will

be half the coefficient of the middle term squared.

So we have (x + 1)² = 5.

Now square root both sides and remember to use plus or minus.

So we have x + 1 = ±√5.

Now subtract 1 form both sides to get x = -1 ± √5.