3X^2-80X+300=0

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Solution for 3X^2-80X+300=0 equation: 


Simplifying
3X2 + -80X + 300 = 0

Reorder the terms:
300 + -80X + 3X2 = 0

Solving
300 + -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'.
100 + -26.66666667X + X2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -26.66666667X + -100 + X2 = 0 + -100

Reorder the terms:
100 + -100 + -26.66666667X + X2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -26.66666667X + X2 = 0 + -100
-26.66666667X + X2 = 0 + -100

Combine like terms: 0 + -100 = -100
-26.66666667X + X2 = -100

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 = -100 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667X + X2 = -100 + 177.7777780

Combine like terms: -100 + 177.7777780 = 77.777778
177.7777780 + -26.66666667X + X2 = 77.777778

Factor a perfect square on the left side:
(X + -13.33333334)(X + -13.33333334) = 77.777778

Calculate the square root of the right side: 8.819171049

Break this problem into two subproblems by setting 
(X + -13.33333334) equal to 8.819171049 and -8.819171049.


Subproblem 1
X + -13.33333334 = 8.819171049

Simplifying
X + -13.33333334 = 8.819171049

Reorder the terms:
-13.33333334 + X = 8.819171049

Solving
-13.33333334 + X = 8.819171049

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 = 8.819171049 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + X = 8.819171049 + 13.33333334
X = 8.819171049 + 13.33333334

Combine like terms: 8.819171049 + 13.33333334 = 22.152504389
X = 22.152504389

Simplifying
X = 22.152504389


Subproblem 2
X + -13.33333334 = -8.819171049

Simplifying
X + -13.33333334 = -8.819171049

Reorder the terms:
-13.33333334 + X = -8.819171049

Solving
-13.33333334 + X = -8.819171049

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 = -8.819171049 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + X = -8.819171049 + 13.33333334
X = -8.819171049 + 13.33333334

Combine like terms: -8.819171049 + 13.33333334 = 4.514162291
X = 4.514162291

Simplifying
X = 4.514162291


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {22.152504389, 4.514162291}

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