Question

Simplify the equation by completing the square
x^2+6x+15=0

Answer 1

x=-3±
`√(6)i`

Explanation:

First, move 15 to the other side by subtracting 15 from both sides:

x^2+6x=-15

Next, figure out what can be added to the left side to make it a perfect square. The number that is added would be a perfect square and would be half of the coefficent of x times itself, meaning that it would be 9. So:

x^2+6x+9=-6

Now we can convert the left side of the equation to a perfect square.

(x+3)^2 = -6

Now, this is the part where it gets weird. I'm not sure if this problem wants you to put no solution if you get an answer like this. But, I'll continue on anyways.

Square root both sides:

x+3=±
`√(-6)`

Subtract three from both sides

x=-3±
`√(-6)`

Since we are squaring by a negative, we add a special kind of i to signify that its imaginary.

x=-3±
`√(6)i`

Therefore, either this is the answer, or just put two separate answers with a plus and minus where that plus and minus symbol is.