3x^2-80x+200=

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Solution for 3x^2-80x+200= equation: 


Simplifying
3x2 + -80x + 200 = 0

Reorder the terms:
200 + -80x + 3x2 = 0

Solving
200 + -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'.
66.66666667 + -26.66666667x + x2 = 0

Move the constant term to the right:

Add '-66.66666667' to each side of the equation.
66.66666667 + -26.66666667x + -66.66666667 + x2 = 0 + -66.66666667

Reorder the terms:
66.66666667 + -66.66666667 + -26.66666667x + x2 = 0 + -66.66666667

Combine like terms: 66.66666667 + -66.66666667 = 0.00000000
0.00000000 + -26.66666667x + x2 = 0 + -66.66666667
-26.66666667x + x2 = 0 + -66.66666667

Combine like terms: 0 + -66.66666667 = -66.66666667
-26.66666667x + x2 = -66.66666667

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 = -66.66666667 + 177.7777780

Reorder the terms:
177.7777780 + -26.66666667x + x2 = -66.66666667 + 177.7777780

Combine like terms: -66.66666667 + 177.7777780 = 111.11111133
177.7777780 + -26.66666667x + x2 = 111.11111133

Factor a perfect square on the left side:
(x + -13.33333334)(x + -13.33333334) = 111.11111133

Calculate the square root of the right side: 10.540925544

Break this problem into two subproblems by setting 
(x + -13.33333334) equal to 10.540925544 and -10.540925544.


Subproblem 1
x + -13.33333334 = 10.540925544

Simplifying
x + -13.33333334 = 10.540925544

Reorder the terms:
-13.33333334 + x = 10.540925544

Solving
-13.33333334 + x = 10.540925544

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 = 10.540925544 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = 10.540925544 + 13.33333334
x = 10.540925544 + 13.33333334

Combine like terms: 10.540925544 + 13.33333334 = 23.874258884
x = 23.874258884

Simplifying
x = 23.874258884


Subproblem 2
x + -13.33333334 = -10.540925544

Simplifying
x + -13.33333334 = -10.540925544

Reorder the terms:
-13.33333334 + x = -10.540925544

Solving
-13.33333334 + x = -10.540925544

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 = -10.540925544 + 13.33333334

Combine like terms: -13.33333334 + 13.33333334 = 0.00000000
0.00000000 + x = -10.540925544 + 13.33333334
x = -10.540925544 + 13.33333334

Combine like terms: -10.540925544 + 13.33333334 = 2.792407796
x = 2.792407796

Simplifying
x = 2.792407796


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.874258884, 2.792407796}

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