18x^2-46x-552=0

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Solution for 18x^2-46x-552=0 equation: 


Simplifying
18x2 + -46x + -552 = 0

Reorder the terms:
-552 + -46x + 18x2 = 0

Solving
-552 + -46x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-276 + -23x + 9x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-276 + -23x + 9x2)' equal to zero and attempt to solve:

Simplifying
-276 + -23x + 9x2 = 0

Solving
-276 + -23x + 9x2 = 0

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

Divide each side by '9'.
-30.66666667 + -2.555555556x + x2 = 0

Move the constant term to the right:

Add '30.66666667' to each side of the equation.
-30.66666667 + -2.555555556x + 30.66666667 + x2 = 0 + 30.66666667

Reorder the terms:
-30.66666667 + 30.66666667 + -2.555555556x + x2 = 0 + 30.66666667

Combine like terms: -30.66666667 + 30.66666667 = 0.00000000
0.00000000 + -2.555555556x + x2 = 0 + 30.66666667
-2.555555556x + x2 = 0 + 30.66666667

Combine like terms: 0 + 30.66666667 = 30.66666667
-2.555555556x + x2 = 30.66666667

The x term is -2.555555556x.  Take half its coefficient (-1.277777778).
Square it (1.632716050) and add it to both sides.

Add '1.632716050' to each side of the equation.
-2.555555556x + 1.632716050 + x2 = 30.66666667 + 1.632716050

Reorder the terms:
1.632716050 + -2.555555556x + x2 = 30.66666667 + 1.632716050

Combine like terms: 30.66666667 + 1.632716050 = 32.29938272
1.632716050 + -2.555555556x + x2 = 32.29938272

Factor a perfect square on the left side:
(x + -1.277777778)(x + -1.277777778) = 32.29938272

Calculate the square root of the right side: 5.683254589

Break this problem into two subproblems by setting 
(x + -1.277777778) equal to 5.683254589 and -5.683254589.


Subproblem 1
x + -1.277777778 = 5.683254589

Simplifying
x + -1.277777778 = 5.683254589

Reorder the terms:
-1.277777778 + x = 5.683254589

Solving
-1.277777778 + x = 5.683254589

Solving for variable 'x'.

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

Add '1.277777778' to each side of the equation.
-1.277777778 + 1.277777778 + x = 5.683254589 + 1.277777778

Combine like terms: -1.277777778 + 1.277777778 = 0.000000000
0.000000000 + x = 5.683254589 + 1.277777778
x = 5.683254589 + 1.277777778

Combine like terms: 5.683254589 + 1.277777778 = 6.961032367
x = 6.961032367

Simplifying
x = 6.961032367


Subproblem 2
x + -1.277777778 = -5.683254589

Simplifying
x + -1.277777778 = -5.683254589

Reorder the terms:
-1.277777778 + x = -5.683254589

Solving
-1.277777778 + x = -5.683254589

Solving for variable 'x'.

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

Add '1.277777778' to each side of the equation.
-1.277777778 + 1.277777778 + x = -5.683254589 + 1.277777778

Combine like terms: -1.277777778 + 1.277777778 = 0.000000000
0.000000000 + x = -5.683254589 + 1.277777778
x = -5.683254589 + 1.277777778

Combine like terms: -5.683254589 + 1.277777778 = -4.405476811
x = -4.405476811

Simplifying
x = -4.405476811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.961032367, -4.405476811}
Solution
x = {6.961032367, -4.405476811}

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