18x^2-7x-33=0

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Solution for 18x^2-7x-33=0 equation: 


Simplifying
18x2 + -7x + -33 = 0

Reorder the terms:
-33 + -7x + 18x2 = 0

Solving
-33 + -7x + 18x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
18 the coefficient of the squared term: 

Divide each side by '18'.
-1.833333333 + -0.3888888889x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + -0.3888888889x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + -0.3888888889x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + -0.3888888889x + x2 = 0 + 1.833333333
-0.3888888889x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
-0.3888888889x + x2 = 1.833333333

The x term is -0.3888888889x.  Take half its coefficient (-0.1944444445).
Square it (0.03780864200) and add it to both sides.

Add '0.03780864200' to each side of the equation.
-0.3888888889x + 0.03780864200 + x2 = 1.833333333 + 0.03780864200

Reorder the terms:
0.03780864200 + -0.3888888889x + x2 = 1.833333333 + 0.03780864200

Combine like terms: 1.833333333 + 0.03780864200 = 1.871141975
0.03780864200 + -0.3888888889x + x2 = 1.871141975

Factor a perfect square on the left side:
(x + -0.1944444445)(x + -0.1944444445) = 1.871141975

Calculate the square root of the right side: 1.367896917

Break this problem into two subproblems by setting 
(x + -0.1944444445) equal to 1.367896917 and -1.367896917.


Subproblem 1
x + -0.1944444445 = 1.367896917

Simplifying
x + -0.1944444445 = 1.367896917

Reorder the terms:
-0.1944444445 + x = 1.367896917

Solving
-0.1944444445 + x = 1.367896917

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.1944444445' to each side of the equation.
-0.1944444445 + 0.1944444445 + x = 1.367896917 + 0.1944444445

Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000
0.0000000000 + x = 1.367896917 + 0.1944444445
x = 1.367896917 + 0.1944444445

Combine like terms: 1.367896917 + 0.1944444445 = 1.5623413615
x = 1.5623413615

Simplifying
x = 1.5623413615


Subproblem 2
x + -0.1944444445 = -1.367896917

Simplifying
x + -0.1944444445 = -1.367896917

Reorder the terms:
-0.1944444445 + x = -1.367896917

Solving
-0.1944444445 + x = -1.367896917

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.1944444445' to each side of the equation.
-0.1944444445 + 0.1944444445 + x = -1.367896917 + 0.1944444445

Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000
0.0000000000 + x = -1.367896917 + 0.1944444445
x = -1.367896917 + 0.1944444445

Combine like terms: -1.367896917 + 0.1944444445 = -1.1734524725
x = -1.1734524725

Simplifying
x = -1.1734524725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5623413615, -1.1734524725}

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