12x^2-1400x+30000=0

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Solution for 12x^2-1400x+30000=0 equation: 


Simplifying
12x2 + -1400x + 30000 = 0

Reorder the terms:
30000 + -1400x + 12x2 = 0

Solving
30000 + -1400x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7500 + -350x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7500 + -350x + 3x2)' equal to zero and attempt to solve:

Simplifying
7500 + -350x + 3x2 = 0

Solving
7500 + -350x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2500 + -116.6666667x + x2 = 0

Move the constant term to the right:

Add '-2500' to each side of the equation.
2500 + -116.6666667x + -2500 + x2 = 0 + -2500

Reorder the terms:
2500 + -2500 + -116.6666667x + x2 = 0 + -2500

Combine like terms: 2500 + -2500 = 0
0 + -116.6666667x + x2 = 0 + -2500
-116.6666667x + x2 = 0 + -2500

Combine like terms: 0 + -2500 = -2500
-116.6666667x + x2 = -2500

The x term is -116.6666667x.  Take half its coefficient (-58.33333335).
Square it (3402.777780) and add it to both sides.

Add '3402.777780' to each side of the equation.
-116.6666667x + 3402.777780 + x2 = -2500 + 3402.777780

Reorder the terms:
3402.777780 + -116.6666667x + x2 = -2500 + 3402.777780

Combine like terms: -2500 + 3402.777780 = 902.77778
3402.777780 + -116.6666667x + x2 = 902.77778

Factor a perfect square on the left side:
(x + -58.33333335)(x + -58.33333335) = 902.77778

Calculate the square root of the right side: 30.046260666

Break this problem into two subproblems by setting 
(x + -58.33333335) equal to 30.046260666 and -30.046260666.


Subproblem 1
x + -58.33333335 = 30.046260666

Simplifying
x + -58.33333335 = 30.046260666

Reorder the terms:
-58.33333335 + x = 30.046260666

Solving
-58.33333335 + x = 30.046260666

Solving for variable 'x'.

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

Add '58.33333335' to each side of the equation.
-58.33333335 + 58.33333335 + x = 30.046260666 + 58.33333335

Combine like terms: -58.33333335 + 58.33333335 = 0.00000000
0.00000000 + x = 30.046260666 + 58.33333335
x = 30.046260666 + 58.33333335

Combine like terms: 30.046260666 + 58.33333335 = 88.379594016
x = 88.379594016

Simplifying
x = 88.379594016


Subproblem 2
x + -58.33333335 = -30.046260666

Simplifying
x + -58.33333335 = -30.046260666

Reorder the terms:
-58.33333335 + x = -30.046260666

Solving
-58.33333335 + x = -30.046260666

Solving for variable 'x'.

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

Add '58.33333335' to each side of the equation.
-58.33333335 + 58.33333335 + x = -30.046260666 + 58.33333335

Combine like terms: -58.33333335 + 58.33333335 = 0.00000000
0.00000000 + x = -30.046260666 + 58.33333335
x = -30.046260666 + 58.33333335

Combine like terms: -30.046260666 + 58.33333335 = 28.287072684
x = 28.287072684

Simplifying
x = 28.287072684


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {88.379594016, 28.287072684}
Solution
x = {88.379594016, 28.287072684}

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