3x^2-38x+88=0

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Solution for 3x^2-38x+88=0 equation: 


Simplifying
3x2 + -38x + 88 = 0

Reorder the terms:
88 + -38x + 3x2 = 0

Solving
88 + -38x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
29.33333333 + -12.66666667x + x2 = 0

Move the constant term to the right:

Add '-29.33333333' to each side of the equation.
29.33333333 + -12.66666667x + -29.33333333 + x2 = 0 + -29.33333333

Reorder the terms:
29.33333333 + -29.33333333 + -12.66666667x + x2 = 0 + -29.33333333

Combine like terms: 29.33333333 + -29.33333333 = 0.00000000
0.00000000 + -12.66666667x + x2 = 0 + -29.33333333
-12.66666667x + x2 = 0 + -29.33333333

Combine like terms: 0 + -29.33333333 = -29.33333333
-12.66666667x + x2 = -29.33333333

The x term is -12.66666667x.  Take half its coefficient (-6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
-12.66666667x + 40.11111113 + x2 = -29.33333333 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667x + x2 = -29.33333333 + 40.11111113

Combine like terms: -29.33333333 + 40.11111113 = 10.7777778
40.11111113 + -12.66666667x + x2 = 10.7777778

Factor a perfect square on the left side:
(x + -6.333333335)(x + -6.333333335) = 10.7777778

Calculate the square root of the right side: 3.282952604

Break this problem into two subproblems by setting 
(x + -6.333333335) equal to 3.282952604 and -3.282952604.


Subproblem 1
x + -6.333333335 = 3.282952604

Simplifying
x + -6.333333335 = 3.282952604

Reorder the terms:
-6.333333335 + x = 3.282952604

Solving
-6.333333335 + x = 3.282952604

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = 3.282952604 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = 3.282952604 + 6.333333335
x = 3.282952604 + 6.333333335

Combine like terms: 3.282952604 + 6.333333335 = 9.616285939
x = 9.616285939

Simplifying
x = 9.616285939


Subproblem 2
x + -6.333333335 = -3.282952604

Simplifying
x + -6.333333335 = -3.282952604

Reorder the terms:
-6.333333335 + x = -3.282952604

Solving
-6.333333335 + x = -3.282952604

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = -3.282952604 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = -3.282952604 + 6.333333335
x = -3.282952604 + 6.333333335

Combine like terms: -3.282952604 + 6.333333335 = 3.050380731
x = 3.050380731

Simplifying
x = 3.050380731


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.616285939, 3.050380731}

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