3x^2-400x+10400=0

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Solution for 3x^2-400x+10400=0 equation: 


Simplifying
3x2 + -400x + 10400 = 0

Reorder the terms:
10400 + -400x + 3x2 = 0

Solving
10400 + -400x + 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'.
3466.666667 + -133.3333333x + x2 = 0

Move the constant term to the right:

Add '-3466.666667' to each side of the equation.
3466.666667 + -133.3333333x + -3466.666667 + x2 = 0 + -3466.666667

Reorder the terms:
3466.666667 + -3466.666667 + -133.3333333x + x2 = 0 + -3466.666667

Combine like terms: 3466.666667 + -3466.666667 = 0.000000
0.000000 + -133.3333333x + x2 = 0 + -3466.666667
-133.3333333x + x2 = 0 + -3466.666667

Combine like terms: 0 + -3466.666667 = -3466.666667
-133.3333333x + x2 = -3466.666667

The x term is -133.3333333x.  Take half its coefficient (-66.66666665).
Square it (4444.444442) and add it to both sides.

Add '4444.444442' to each side of the equation.
-133.3333333x + 4444.444442 + x2 = -3466.666667 + 4444.444442

Reorder the terms:
4444.444442 + -133.3333333x + x2 = -3466.666667 + 4444.444442

Combine like terms: -3466.666667 + 4444.444442 = 977.777775
4444.444442 + -133.3333333x + x2 = 977.777775

Factor a perfect square on the left side:
(x + -66.66666665)(x + -66.66666665) = 977.777775

Calculate the square root of the right side: 31.269438354

Break this problem into two subproblems by setting 
(x + -66.66666665) equal to 31.269438354 and -31.269438354.


Subproblem 1
x + -66.66666665 = 31.269438354

Simplifying
x + -66.66666665 = 31.269438354

Reorder the terms:
-66.66666665 + x = 31.269438354

Solving
-66.66666665 + x = 31.269438354

Solving for variable 'x'.

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

Add '66.66666665' to each side of the equation.
-66.66666665 + 66.66666665 + x = 31.269438354 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + x = 31.269438354 + 66.66666665
x = 31.269438354 + 66.66666665

Combine like terms: 31.269438354 + 66.66666665 = 97.936105004
x = 97.936105004

Simplifying
x = 97.936105004


Subproblem 2
x + -66.66666665 = -31.269438354

Simplifying
x + -66.66666665 = -31.269438354

Reorder the terms:
-66.66666665 + x = -31.269438354

Solving
-66.66666665 + x = -31.269438354

Solving for variable 'x'.

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

Add '66.66666665' to each side of the equation.
-66.66666665 + 66.66666665 + x = -31.269438354 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + x = -31.269438354 + 66.66666665
x = -31.269438354 + 66.66666665

Combine like terms: -31.269438354 + 66.66666665 = 35.397228296
x = 35.397228296

Simplifying
x = 35.397228296


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {97.936105004, 35.397228296}

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