Answer:
We can start by subtracting 6 from both sides of the equation:
x^2 + 6 - 6 = -10x - 6
x^2 = -10x - 12
To complete the square, we need to add and subtract the same value so that the left side of the equation is a perfect square. In this case, we need to add and subtract (1/2)(10)^2 = 25/2:
x^2 = -10x - 12 + 25/2 - 25/2
(x^2 + 10x + 25/2) = 25/2 - 12
(x^2 + 10x + 25/2) = -24/2
Now we can take the square root of both sides, and we get:
x + 5/2 = ± √(-24/2)
The square root of a negative number is an imaginary number, so we can't simplify this equation any further. This means that there are no real solutions to this equation.
Explanation: