-12x^2+420x+13400=0

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Solution for -12x^2+420x+13400=0 equation: 


Simplifying
-12x2 + 420x + 13400 = 0

Reorder the terms:
13400 + 420x + -12x2 = 0

Solving
13400 + 420x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3350 + 105x + -3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3350 + 105x + -3x2)' equal to zero and attempt to solve:

Simplifying
3350 + 105x + -3x2 = 0

Solving
3350 + 105x + -3x2 = 0

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

Divide each side by '-3'.
-1116.666667 + -35x + x2 = 0

Move the constant term to the right:

Add '1116.666667' to each side of the equation.
-1116.666667 + -35x + 1116.666667 + x2 = 0 + 1116.666667

Reorder the terms:
-1116.666667 + 1116.666667 + -35x + x2 = 0 + 1116.666667

Combine like terms: -1116.666667 + 1116.666667 = 0.000000
0.000000 + -35x + x2 = 0 + 1116.666667
-35x + x2 = 0 + 1116.666667

Combine like terms: 0 + 1116.666667 = 1116.666667
-35x + x2 = 1116.666667

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = 1116.666667 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 1116.666667 + 306.25

Combine like terms: 1116.666667 + 306.25 = 1422.916667
306.25 + -35x + x2 = 1422.916667

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 1422.916667

Calculate the square root of the right side: 37.721567664

Break this problem into two subproblems by setting 
(x + -17.5) equal to 37.721567664 and -37.721567664.


Subproblem 1
x + -17.5 = 37.721567664

Simplifying
x + -17.5 = 37.721567664

Reorder the terms:
-17.5 + x = 37.721567664

Solving
-17.5 + x = 37.721567664

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 37.721567664 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 37.721567664 + 17.5
x = 37.721567664 + 17.5

Combine like terms: 37.721567664 + 17.5 = 55.221567664
x = 55.221567664

Simplifying
x = 55.221567664


Subproblem 2
x + -17.5 = -37.721567664

Simplifying
x + -17.5 = -37.721567664

Reorder the terms:
-17.5 + x = -37.721567664

Solving
-17.5 + x = -37.721567664

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -37.721567664 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -37.721567664 + 17.5
x = -37.721567664 + 17.5

Combine like terms: -37.721567664 + 17.5 = -20.221567664
x = -20.221567664

Simplifying
x = -20.221567664


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {55.221567664, -20.221567664}
Solution
x = {55.221567664, -20.221567664}

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