120x+50x(230-x)=17100

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Solution for 120x+50x(230-x)=17100 equation:


Simplifying
120x + 50x(230 + -1x) = 17100
120x + (230 * 50x + -1x * 50x) = 17100
120x + (11500x + -50x2) = 17100

Combine like terms: 120x + 11500x = 11620x
11620x + -50x2 = 17100

Solving
11620x + -50x2 = 17100

Solving for variable 'x'.

Reorder the terms:
-17100 + 11620x + -50x2 = 17100 + -17100

Combine like terms: 17100 + -17100 = 0
-17100 + 11620x + -50x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-1710 + 1162x + -5x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-1710 + 1162x + -5x2)' equal to zero and attempt to solve:

Simplifying
-1710 + 1162x + -5x2 = 0

Solving
-1710 + 1162x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
342 + -232.4x + x2 = 0

Move the constant term to the right:

Add '-342' to each side of the equation.
342 + -232.4x + -342 + x2 = 0 + -342

Reorder the terms:
342 + -342 + -232.4x + x2 = 0 + -342

Combine like terms: 342 + -342 = 0
0 + -232.4x + x2 = 0 + -342
-232.4x + x2 = 0 + -342

Combine like terms: 0 + -342 = -342
-232.4x + x2 = -342

The x term is -232.4x.  Take half its coefficient (-116.2).
Square it (13502.44) and add it to both sides.

Add '13502.44' to each side of the equation.
-232.4x + 13502.44 + x2 = -342 + 13502.44

Reorder the terms:
13502.44 + -232.4x + x2 = -342 + 13502.44

Combine like terms: -342 + 13502.44 = 13160.44
13502.44 + -232.4x + x2 = 13160.44

Factor a perfect square on the left side:
(x + -116.2)(x + -116.2) = 13160.44

Calculate the square root of the right side: 114.718960944

Break this problem into two subproblems by setting 
(x + -116.2) equal to 114.718960944 and -114.718960944.


Subproblem 1
x + -116.2 = 114.718960944

Simplifying
x + -116.2 = 114.718960944

Reorder the terms:
-116.2 + x = 114.718960944

Solving
-116.2 + x = 114.718960944

Solving for variable 'x'.

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

Add '116.2' to each side of the equation.
-116.2 + 116.2 + x = 114.718960944 + 116.2

Combine like terms: -116.2 + 116.2 = 0.0
0.0 + x = 114.718960944 + 116.2
x = 114.718960944 + 116.2

Combine like terms: 114.718960944 + 116.2 = 230.918960944
x = 230.918960944

Simplifying
x = 230.918960944


Subproblem 2
x + -116.2 = -114.718960944

Simplifying
x + -116.2 = -114.718960944

Reorder the terms:
-116.2 + x = -114.718960944

Solving
-116.2 + x = -114.718960944

Solving for variable 'x'.

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

Add '116.2' to each side of the equation.
-116.2 + 116.2 + x = -114.718960944 + 116.2

Combine like terms: -116.2 + 116.2 = 0.0
0.0 + x = -114.718960944 + 116.2
x = -114.718960944 + 116.2

Combine like terms: -114.718960944 + 116.2 = 1.481039056
x = 1.481039056

Simplifying
x = 1.481039056


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {230.918960944, 1.481039056}
Solution
x = {230.918960944, 1.481039056}

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