100.80(2x)+55x(3x)=36600

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Solution for 100.80(2x)+55x(3x)=36600 equation:


Simplifying
100.80(2x) + 55x(3x) = 36600

Remove parenthesis around (2x)
100.80 * 2x + 55x(3x) = 36600

Multiply 100.80 * 2
201.6x + 55x(3x) = 36600

Remove parenthesis around (3x)
201.6x + 55x * 3x = 36600

Reorder the terms for easier multiplication:
201.6x + 55 * 3x * x = 36600

Multiply 55 * 3
201.6x + 165x * x = 36600

Multiply x * x
201.6x + 165x2 = 36600

Solving
201.6x + 165x2 = 36600

Solving for variable 'x'.

Reorder the terms:
-36600 + 201.6x + 165x2 = 36600 + -36600

Combine like terms: 36600 + -36600 = 0
-36600 + 201.6x + 165x2 = 0

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

Divide each side by '165'.
-221.8181818 + 1.221818182x + x2 = 0

Move the constant term to the right:

Add '221.8181818' to each side of the equation.
-221.8181818 + 1.221818182x + 221.8181818 + x2 = 0 + 221.8181818

Reorder the terms:
-221.8181818 + 221.8181818 + 1.221818182x + x2 = 0 + 221.8181818

Combine like terms: -221.8181818 + 221.8181818 = 0.0000000
0.0000000 + 1.221818182x + x2 = 0 + 221.8181818
1.221818182x + x2 = 0 + 221.8181818

Combine like terms: 0 + 221.8181818 = 221.8181818
1.221818182x + x2 = 221.8181818

The x term is 1.221818182x.  Take half its coefficient (0.610909091).
Square it (0.3732099175) and add it to both sides.

Add '0.3732099175' to each side of the equation.
1.221818182x + 0.3732099175 + x2 = 221.8181818 + 0.3732099175

Reorder the terms:
0.3732099175 + 1.221818182x + x2 = 221.8181818 + 0.3732099175

Combine like terms: 221.8181818 + 0.3732099175 = 222.1913917175
0.3732099175 + 1.221818182x + x2 = 222.1913917175

Factor a perfect square on the left side:
(x + 0.610909091)(x + 0.610909091) = 222.1913917175

Calculate the square root of the right side: 14.906085728

Break this problem into two subproblems by setting 
(x + 0.610909091) equal to 14.906085728 and -14.906085728.

Subproblem 1

x + 0.610909091 = 14.906085728 Simplifying x + 0.610909091 = 14.906085728 Reorder the terms: 0.610909091 + x = 14.906085728 Solving 0.610909091 + x = 14.906085728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.610909091' to each side of the equation. 0.610909091 + -0.610909091 + x = 14.906085728 + -0.610909091 Combine like terms: 0.610909091 + -0.610909091 = 0.000000000 0.000000000 + x = 14.906085728 + -0.610909091 x = 14.906085728 + -0.610909091 Combine like terms: 14.906085728 + -0.610909091 = 14.295176637 x = 14.295176637 Simplifying x = 14.295176637

Subproblem 2

x + 0.610909091 = -14.906085728 Simplifying x + 0.610909091 = -14.906085728 Reorder the terms: 0.610909091 + x = -14.906085728 Solving 0.610909091 + x = -14.906085728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.610909091' to each side of the equation. 0.610909091 + -0.610909091 + x = -14.906085728 + -0.610909091 Combine like terms: 0.610909091 + -0.610909091 = 0.000000000 0.000000000 + x = -14.906085728 + -0.610909091 x = -14.906085728 + -0.610909091 Combine like terms: -14.906085728 + -0.610909091 = -15.516994819 x = -15.516994819 Simplifying x = -15.516994819

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.295176637, -15.516994819}

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