3x^2-370x+5000=0

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Solution for 3x^2-370x+5000=0 equation: 


Simplifying
3x2 + -370x + 5000 = 0

Reorder the terms:
5000 + -370x + 3x2 = 0

Solving
5000 + -370x + 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'.
1666.666667 + -123.3333333x + x2 = 0

Move the constant term to the right:

Add '-1666.666667' to each side of the equation.
1666.666667 + -123.3333333x + -1666.666667 + x2 = 0 + -1666.666667

Reorder the terms:
1666.666667 + -1666.666667 + -123.3333333x + x2 = 0 + -1666.666667

Combine like terms: 1666.666667 + -1666.666667 = 0.000000
0.000000 + -123.3333333x + x2 = 0 + -1666.666667
-123.3333333x + x2 = 0 + -1666.666667

Combine like terms: 0 + -1666.666667 = -1666.666667
-123.3333333x + x2 = -1666.666667

The x term is -123.3333333x.  Take half its coefficient (-61.66666665).
Square it (3802.777776) and add it to both sides.

Add '3802.777776' to each side of the equation.
-123.3333333x + 3802.777776 + x2 = -1666.666667 + 3802.777776

Reorder the terms:
3802.777776 + -123.3333333x + x2 = -1666.666667 + 3802.777776

Combine like terms: -1666.666667 + 3802.777776 = 2136.111109
3802.777776 + -123.3333333x + x2 = 2136.111109

Factor a perfect square on the left side:
(x + -61.66666665)(x + -61.66666665) = 2136.111109

Calculate the square root of the right side: 46.218082057

Break this problem into two subproblems by setting 
(x + -61.66666665) equal to 46.218082057 and -46.218082057.


Subproblem 1
x + -61.66666665 = 46.218082057

Simplifying
x + -61.66666665 = 46.218082057

Reorder the terms:
-61.66666665 + x = 46.218082057

Solving
-61.66666665 + x = 46.218082057

Solving for variable 'x'.

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

Add '61.66666665' to each side of the equation.
-61.66666665 + 61.66666665 + x = 46.218082057 + 61.66666665

Combine like terms: -61.66666665 + 61.66666665 = 0.00000000
0.00000000 + x = 46.218082057 + 61.66666665
x = 46.218082057 + 61.66666665

Combine like terms: 46.218082057 + 61.66666665 = 107.884748707
x = 107.884748707

Simplifying
x = 107.884748707


Subproblem 2
x + -61.66666665 = -46.218082057

Simplifying
x + -61.66666665 = -46.218082057

Reorder the terms:
-61.66666665 + x = -46.218082057

Solving
-61.66666665 + x = -46.218082057

Solving for variable 'x'.

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

Add '61.66666665' to each side of the equation.
-61.66666665 + 61.66666665 + x = -46.218082057 + 61.66666665

Combine like terms: -61.66666665 + 61.66666665 = 0.00000000
0.00000000 + x = -46.218082057 + 61.66666665
x = -46.218082057 + 61.66666665

Combine like terms: -46.218082057 + 61.66666665 = 15.448584593
x = 15.448584593

Simplifying
x = 15.448584593


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {107.884748707, 15.448584593}

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