3x^2+155x-8=0

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Solution for 3x^2+155x-8=0 equation: 


Simplifying
3x2 + 155x + -8 = 0

Reorder the terms:
-8 + 155x + 3x2 = 0

Solving
-8 + 155x + 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'.
-2.666666667 + 51.66666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 51.66666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 51.66666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 51.66666667x + x2 = 0 + 2.666666667
51.66666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
51.66666667x + x2 = 2.666666667

The x term is 51.66666667x.  Take half its coefficient (25.83333334).
Square it (667.3611115) and add it to both sides.

Add '667.3611115' to each side of the equation.
51.66666667x + 667.3611115 + x2 = 2.666666667 + 667.3611115

Reorder the terms:
667.3611115 + 51.66666667x + x2 = 2.666666667 + 667.3611115

Combine like terms: 2.666666667 + 667.3611115 = 670.027778167
667.3611115 + 51.66666667x + x2 = 670.027778167

Factor a perfect square on the left side:
(x + 25.83333334)(x + 25.83333334) = 670.027778167

Calculate the square root of the right side: 25.884894788

Break this problem into two subproblems by setting 
(x + 25.83333334) equal to 25.884894788 and -25.884894788.


Subproblem 1
x + 25.83333334 = 25.884894788

Simplifying
x + 25.83333334 = 25.884894788

Reorder the terms:
25.83333334 + x = 25.884894788

Solving
25.83333334 + x = 25.884894788

Solving for variable 'x'.

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

Add '-25.83333334' to each side of the equation.
25.83333334 + -25.83333334 + x = 25.884894788 + -25.83333334

Combine like terms: 25.83333334 + -25.83333334 = 0.00000000
0.00000000 + x = 25.884894788 + -25.83333334
x = 25.884894788 + -25.83333334

Combine like terms: 25.884894788 + -25.83333334 = 0.051561448
x = 0.051561448

Simplifying
x = 0.051561448


Subproblem 2
x + 25.83333334 = -25.884894788

Simplifying
x + 25.83333334 = -25.884894788

Reorder the terms:
25.83333334 + x = -25.884894788

Solving
25.83333334 + x = -25.884894788

Solving for variable 'x'.

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

Add '-25.83333334' to each side of the equation.
25.83333334 + -25.83333334 + x = -25.884894788 + -25.83333334

Combine like terms: 25.83333334 + -25.83333334 = 0.00000000
0.00000000 + x = -25.884894788 + -25.83333334
x = -25.884894788 + -25.83333334

Combine like terms: -25.884894788 + -25.83333334 = -51.718228128
x = -51.718228128

Simplifying
x = -51.718228128


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.051561448, -51.718228128}

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