Answer: ∅
Step-by-step explanation: When solving by completing the square,
we cannot have a coefficient on the squared term.
So first divide both sides by 4 to get x² + 4x + 25/4 = 0.
Now subtract 25/4 from both sides and leave a space.
So we have x² + 4x ____ = -25/4 ____.
The number that goes in that space is the number needed
to create a perfect square trinomial on the left side.
The question is, what is that number?
Well it comes from a formula.
The number that goes in that space comes from
half the coefficient of the middle term squared.
So that's half of 4 squared or 2 squared which is 4.
So we add 4 to both sides.
On the left, we will get a binomial squared
which will use x and half the coefficient of the middle term.
So we have (x + 2)².
On the right, -25/4 + 16/4 is -9/4.
So we have (x + 2)² = -9/4.
Notice that when take the square root of both sides,
we have the square root of a negative which is illegal.
So we say our answer is ∅.
