3x(750-2x)=1750

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Solution for 3x(750-2x)=1750 equation: 


Simplifying
3x(750 + -2x) = 1750
(750 * 3x + -2x * 3x) = 1750
(2250x + -6x2) = 1750

Solving
2250x + -6x2 = 1750

Solving for variable 'x'.

Reorder the terms:
-1750 + 2250x + -6x2 = 1750 + -1750

Combine like terms: 1750 + -1750 = 0
-1750 + 2250x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-875 + 1125x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-875 + 1125x + -3x2)' equal to zero and attempt to solve:

Simplifying
-875 + 1125x + -3x2 = 0

Solving
-875 + 1125x + -3x2 = 0

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

Divide each side by '-3'.
291.6666667 + -375x + x2 = 0

Move the constant term to the right:

Add '-291.6666667' to each side of the equation.
291.6666667 + -375x + -291.6666667 + x2 = 0 + -291.6666667

Reorder the terms:
291.6666667 + -291.6666667 + -375x + x2 = 0 + -291.6666667

Combine like terms: 291.6666667 + -291.6666667 = 0.0000000
0.0000000 + -375x + x2 = 0 + -291.6666667
-375x + x2 = 0 + -291.6666667

Combine like terms: 0 + -291.6666667 = -291.6666667
-375x + x2 = -291.6666667

The x term is -375x.  Take half its coefficient (-187.5).
Square it (35156.25) and add it to both sides.

Add '35156.25' to each side of the equation.
-375x + 35156.25 + x2 = -291.6666667 + 35156.25

Reorder the terms:
35156.25 + -375x + x2 = -291.6666667 + 35156.25

Combine like terms: -291.6666667 + 35156.25 = 34864.5833333
35156.25 + -375x + x2 = 34864.5833333

Factor a perfect square on the left side:
(x + -187.5)(x + -187.5) = 34864.5833333

Calculate the square root of the right side: 186.720602327

Break this problem into two subproblems by setting 
(x + -187.5) equal to 186.720602327 and -186.720602327.


Subproblem 1
x + -187.5 = 186.720602327

Simplifying
x + -187.5 = 186.720602327

Reorder the terms:
-187.5 + x = 186.720602327

Solving
-187.5 + x = 186.720602327

Solving for variable 'x'.

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

Add '187.5' to each side of the equation.
-187.5 + 187.5 + x = 186.720602327 + 187.5

Combine like terms: -187.5 + 187.5 = 0.0
0.0 + x = 186.720602327 + 187.5
x = 186.720602327 + 187.5

Combine like terms: 186.720602327 + 187.5 = 374.220602327
x = 374.220602327

Simplifying
x = 374.220602327


Subproblem 2
x + -187.5 = -186.720602327

Simplifying
x + -187.5 = -186.720602327

Reorder the terms:
-187.5 + x = -186.720602327

Solving
-187.5 + x = -186.720602327

Solving for variable 'x'.

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

Add '187.5' to each side of the equation.
-187.5 + 187.5 + x = -186.720602327 + 187.5

Combine like terms: -187.5 + 187.5 = 0.0
0.0 + x = -186.720602327 + 187.5
x = -186.720602327 + 187.5

Combine like terms: -186.720602327 + 187.5 = 0.779397673
x = 0.779397673

Simplifying
x = 0.779397673


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {374.220602327, 0.779397673}
Solution
x = {374.220602327, 0.779397673}

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