Question

Solve by completing the square: 4x^2 + 16x +25 =0 x = _ & x = _

Answer 1

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 ∅.