Q:

Solve by completing the square x^2+ 18x+93=0

Accepted Solution

A:
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