.12x(3x+30000)=38160

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Solution for .12x(3x+30000)=38160 equation:


Simplifying
0.12x(3x + 30000) = 38160

Reorder the terms:
0.12x(30000 + 3x) = 38160
(30000 * 0.12x + 3x * 0.12x) = 38160
(3600x + 0.36x2) = 38160

Solving
3600x + 0.36x2 = 38160

Solving for variable 'x'.

Reorder the terms:
-38160 + 3600x + 0.36x2 = 38160 + -38160

Combine like terms: 38160 + -38160 = 0
-38160 + 3600x + 0.36x2 = 0

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

Divide each side by '0.36'.
-106000 + 10000x + x2 = 0

Move the constant term to the right:

Add '106000' to each side of the equation.
-106000 + 10000x + 106000 + x2 = 0 + 106000

Reorder the terms:
-106000 + 106000 + 10000x + x2 = 0 + 106000

Combine like terms: -106000 + 106000 = 0
0 + 10000x + x2 = 0 + 106000
10000x + x2 = 0 + 106000

Combine like terms: 0 + 106000 = 106000
10000x + x2 = 106000

The x term is 10000x.  Take half its coefficient (5000).
Square it (25000000) and add it to both sides.

Add '25000000' to each side of the equation.
10000x + 25000000 + x2 = 106000 + 25000000

Reorder the terms:
25000000 + 10000x + x2 = 106000 + 25000000

Combine like terms: 106000 + 25000000 = 25106000
25000000 + 10000x + x2 = 25106000

Factor a perfect square on the left side:
(x + 5000)(x + 5000) = 25106000

Calculate the square root of the right side: 5010.588787757

Break this problem into two subproblems by setting 
(x + 5000) equal to 5010.588787757 and -5010.588787757.

Subproblem 1

x + 5000 = 5010.588787757 Simplifying x + 5000 = 5010.588787757 Reorder the terms: 5000 + x = 5010.588787757 Solving 5000 + x = 5010.588787757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5000' to each side of the equation. 5000 + -5000 + x = 5010.588787757 + -5000 Combine like terms: 5000 + -5000 = 0 0 + x = 5010.588787757 + -5000 x = 5010.588787757 + -5000 Combine like terms: 5010.588787757 + -5000 = 10.588787757 x = 10.588787757 Simplifying x = 10.588787757

Subproblem 2

x + 5000 = -5010.588787757 Simplifying x + 5000 = -5010.588787757 Reorder the terms: 5000 + x = -5010.588787757 Solving 5000 + x = -5010.588787757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5000' to each side of the equation. 5000 + -5000 + x = -5010.588787757 + -5000 Combine like terms: 5000 + -5000 = 0 0 + x = -5010.588787757 + -5000 x = -5010.588787757 + -5000 Combine like terms: -5010.588787757 + -5000 = -10010.588787757 x = -10010.588787757 Simplifying x = -10010.588787757

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.588787757, -10010.588787757}

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