3x^2-80x+310=0

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Solution for 3x^2-80x+310=0 equation: 


Simplifying
3x2 + -80x + 310 = 0

Reorder the terms:
310 + -80x + 3x2 = 0

Solving
310 + -80x + 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'.
103.3333333 + -26.66666667x + x2 = 0

Move the constant term to the right:

Add '-103.3333333' to each side of the equation.
103.3333333 + -26.66666667x + -103.3333333 + x2 = 0 + -103.3333333

Reorder the terms:
103.3333333 + -103.3333333 + -26.66666667x + x2 = 0 + -103.3333333

Combine like terms: 103.3333333 + -103.3333333 = 0.0000000
0.0000000 + -26.66666667x + x2 = 0 + -103.3333333
-26.66666667x + x2 = 0 + -103.3333333

Combine like terms: 0 + -103.3333333 = -103.3333333
-26.66666667x + x2 = -103.3333333

The x term is -26.66666667x.  Take half its coefficient (-13.33333334).
Square it (177.7777780) and add it to both sides.

Add '177.7777780' to each side of the equation.
-26.66666667x + 177.7777780 + x2 = -103.3333333 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667x + x2 = -103.3333333 + 177.7777780

Combine like terms: -103.3333333 + 177.7777780 = 74.4444447
177.7777780 + -26.66666667x + x2 = 74.4444447

Factor a perfect square on the left side:
(x + -13.33333334)(x + -13.33333334) = 74.4444447

Calculate the square root of the right side: 8.628119419

Break this problem into two subproblems by setting 
(x + -13.33333334) equal to 8.628119419 and -8.628119419.


Subproblem 1
x + -13.33333334 = 8.628119419

Simplifying
x + -13.33333334 = 8.628119419

Reorder the terms:
-13.33333334 + x = 8.628119419

Solving
-13.33333334 + x = 8.628119419

Solving for variable 'x'.

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

Add '13.33333334' to each side of the equation.
-13.33333334 + 13.33333334 + x = 8.628119419 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = 8.628119419 + 13.33333334
x = 8.628119419 + 13.33333334

Combine like terms: 8.628119419 + 13.33333334 = 21.961452759
x = 21.961452759

Simplifying
x = 21.961452759


Subproblem 2
x + -13.33333334 = -8.628119419

Simplifying
x + -13.33333334 = -8.628119419

Reorder the terms:
-13.33333334 + x = -8.628119419

Solving
-13.33333334 + x = -8.628119419

Solving for variable 'x'.

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

Add '13.33333334' to each side of the equation.
-13.33333334 + 13.33333334 + x = -8.628119419 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = -8.628119419 + 13.33333334
x = -8.628119419 + 13.33333334

Combine like terms: -8.628119419 + 13.33333334 = 4.705213921
x = 4.705213921

Simplifying
x = 4.705213921


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.961452759, 4.705213921}

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