-3x^2+400x+5201=0

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Solution for -3x^2+400x+5201=0 equation: 


Simplifying
-3x2 + 400x + 5201 = 0

Reorder the terms:
5201 + 400x + -3x2 = 0

Solving
5201 + 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'.
-1733.666667 + -133.3333333x + x2 = 0

Move the constant term to the right:

Add '1733.666667' to each side of the equation.
-1733.666667 + -133.3333333x + 1733.666667 + x2 = 0 + 1733.666667

Reorder the terms:
-1733.666667 + 1733.666667 + -133.3333333x + x2 = 0 + 1733.666667

Combine like terms: -1733.666667 + 1733.666667 = 0.000000
0.000000 + -133.3333333x + x2 = 0 + 1733.666667
-133.3333333x + x2 = 0 + 1733.666667

Combine like terms: 0 + 1733.666667 = 1733.666667
-133.3333333x + x2 = 1733.666667

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 = 1733.666667 + 4444.444442

Reorder the terms:
4444.444442 + -133.3333333x + x2 = 1733.666667 + 4444.444442

Combine like terms: 1733.666667 + 4444.444442 = 6178.111109
4444.444442 + -133.3333333x + x2 = 6178.111109

Factor a perfect square on the left side:
(x + -66.66666665)(x + -66.66666665) = 6178.111109

Calculate the square root of the right side: 78.600961247

Break this problem into two subproblems by setting 
(x + -66.66666665) equal to 78.600961247 and -78.600961247.


Subproblem 1
x + -66.66666665 = 78.600961247

Simplifying
x + -66.66666665 = 78.600961247

Reorder the terms:
-66.66666665 + x = 78.600961247

Solving
-66.66666665 + x = 78.600961247

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 = 78.600961247 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + x = 78.600961247 + 66.66666665
x = 78.600961247 + 66.66666665

Combine like terms: 78.600961247 + 66.66666665 = 145.267627897
x = 145.267627897

Simplifying
x = 145.267627897


Subproblem 2
x + -66.66666665 = -78.600961247

Simplifying
x + -66.66666665 = -78.600961247

Reorder the terms:
-66.66666665 + x = -78.600961247

Solving
-66.66666665 + x = -78.600961247

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 = -78.600961247 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + x = -78.600961247 + 66.66666665
x = -78.600961247 + 66.66666665

Combine like terms: -78.600961247 + 66.66666665 = -11.934294597
x = -11.934294597

Simplifying
x = -11.934294597


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {145.267627897, -11.934294597}

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