x(340-2x)=5600

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Solution for x(340-2x)=5600 equation: 


Simplifying
x(340 + -2x) = 5600
(340 * x + -2x * x) = 5600
(340x + -2x2) = 5600

Solving
340x + -2x2 = 5600

Solving for variable 'x'.

Reorder the terms:
-5600 + 340x + -2x2 = 5600 + -5600

Combine like terms: 5600 + -5600 = 0
-5600 + 340x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2800 + 170x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2800 + 170x + -1x2)' equal to zero and attempt to solve:

Simplifying
-2800 + 170x + -1x2 = 0

Solving
-2800 + 170x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2800 + -170x + x2 = 0

Move the constant term to the right:

Add '-2800' to each side of the equation.
2800 + -170x + -2800 + x2 = 0 + -2800

Reorder the terms:
2800 + -2800 + -170x + x2 = 0 + -2800

Combine like terms: 2800 + -2800 = 0
0 + -170x + x2 = 0 + -2800
-170x + x2 = 0 + -2800

Combine like terms: 0 + -2800 = -2800
-170x + x2 = -2800

The x term is -170x.  Take half its coefficient (-85).
Square it (7225) and add it to both sides.

Add '7225' to each side of the equation.
-170x + 7225 + x2 = -2800 + 7225

Reorder the terms:
7225 + -170x + x2 = -2800 + 7225

Combine like terms: -2800 + 7225 = 4425
7225 + -170x + x2 = 4425

Factor a perfect square on the left side:
(x + -85)(x + -85) = 4425

Calculate the square root of the right side: 66.520673478

Break this problem into two subproblems by setting 
(x + -85) equal to 66.520673478 and -66.520673478.


Subproblem 1
x + -85 = 66.520673478

Simplifying
x + -85 = 66.520673478

Reorder the terms:
-85 + x = 66.520673478

Solving
-85 + x = 66.520673478

Solving for variable 'x'.

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

Add '85' to each side of the equation.
-85 + 85 + x = 66.520673478 + 85

Combine like terms: -85 + 85 = 0
0 + x = 66.520673478 + 85
x = 66.520673478 + 85

Combine like terms: 66.520673478 + 85 = 151.520673478
x = 151.520673478

Simplifying
x = 151.520673478


Subproblem 2
x + -85 = -66.520673478

Simplifying
x + -85 = -66.520673478

Reorder the terms:
-85 + x = -66.520673478

Solving
-85 + x = -66.520673478

Solving for variable 'x'.

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

Add '85' to each side of the equation.
-85 + 85 + x = -66.520673478 + 85

Combine like terms: -85 + 85 = 0
0 + x = -66.520673478 + 85
x = -66.520673478 + 85

Combine like terms: -66.520673478 + 85 = 18.479326522
x = 18.479326522

Simplifying
x = 18.479326522


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {151.520673478, 18.479326522}
Solution
x = {151.520673478, 18.479326522}

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