The equation given above is written below,
x² + 18x + 93 = 0
First step to completing the square is to transpose the constant to the right-hand side of the equation.
x² + 18x = -93
Then, the complete square should take the form,
x² + 18x + ____ = -93 + ___
To determine the number that should be written in the blanks, divide the numerical coefficient of the second term and square the quotient.
___ = (18/2)^2 = 91
The complete square should become,
x² + 18x + 91 = -93 + 91 = -2
(x + 9)^2 = -2
By extracting the squares,
x + 9 = sqrt (-2)
The roots of the equations are two same,
x = sqrt(-2) - 9