3x^2-80x+290=0

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Solution for 3x^2-80x+290=0 equation: 


Simplifying
3x2 + -80x + 290 = 0

Reorder the terms:
290 + -80x + 3x2 = 0

Solving
290 + -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'.
96.66666667 + -26.66666667x + x2 = 0

Move the constant term to the right:

Add '-96.66666667' to each side of the equation.
96.66666667 + -26.66666667x + -96.66666667 + x2 = 0 + -96.66666667

Reorder the terms:
96.66666667 + -96.66666667 + -26.66666667x + x2 = 0 + -96.66666667

Combine like terms: 96.66666667 + -96.66666667 = 0.00000000
0.00000000 + -26.66666667x + x2 = 0 + -96.66666667
-26.66666667x + x2 = 0 + -96.66666667

Combine like terms: 0 + -96.66666667 = -96.66666667
-26.66666667x + x2 = -96.66666667

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 = -96.66666667 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667x + x2 = -96.66666667 + 177.7777780

Combine like terms: -96.66666667 + 177.7777780 = 81.11111133
177.7777780 + -26.66666667x + x2 = 81.11111133

Factor a perfect square on the left side:
(x + -13.33333334)(x + -13.33333334) = 81.11111133

Calculate the square root of the right side: 9.006170736

Break this problem into two subproblems by setting 
(x + -13.33333334) equal to 9.006170736 and -9.006170736.


Subproblem 1
x + -13.33333334 = 9.006170736

Simplifying
x + -13.33333334 = 9.006170736

Reorder the terms:
-13.33333334 + x = 9.006170736

Solving
-13.33333334 + x = 9.006170736

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 = 9.006170736 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = 9.006170736 + 13.33333334
x = 9.006170736 + 13.33333334

Combine like terms: 9.006170736 + 13.33333334 = 22.339504076
x = 22.339504076

Simplifying
x = 22.339504076


Subproblem 2
x + -13.33333334 = -9.006170736

Simplifying
x + -13.33333334 = -9.006170736

Reorder the terms:
-13.33333334 + x = -9.006170736

Solving
-13.33333334 + x = -9.006170736

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 = -9.006170736 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = -9.006170736 + 13.33333334
x = -9.006170736 + 13.33333334

Combine like terms: -9.006170736 + 13.33333334 = 4.327162604
x = 4.327162604

Simplifying
x = 4.327162604


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.339504076, 4.327162604}

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