x(28-2x)=50

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Solution for x(28-2x)=50 equation: 


Simplifying
x(28 + -2x) = 50
(28 * x + -2x * x) = 50
(28x + -2x2) = 50

Solving
28x + -2x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + 28x + -2x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 28x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 14x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 14x + -1x2)' equal to zero and attempt to solve:

Simplifying
-25 + 14x + -1x2 = 0

Solving
-25 + 14x + -1x2 = 0

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

Divide each side by '-1'.
25 + -14x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -14x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -14x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -14x + x2 = 0 + -25
-14x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-14x + x2 = -25

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -25 + 49

Reorder the terms:
49 + -14x + x2 = -25 + 49

Combine like terms: -25 + 49 = 24
49 + -14x + x2 = 24

Factor a perfect square on the left side:
(x + -7)(x + -7) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -7) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + -7 = 4.898979486

Simplifying
x + -7 = 4.898979486

Reorder the terms:
-7 + x = 4.898979486

Solving
-7 + x = 4.898979486

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 4.898979486 + 7

Combine like terms: -7 + 7 = 0
0 + x = 4.898979486 + 7
x = 4.898979486 + 7

Combine like terms: 4.898979486 + 7 = 11.898979486
x = 11.898979486

Simplifying
x = 11.898979486


Subproblem 2
x + -7 = -4.898979486

Simplifying
x + -7 = -4.898979486

Reorder the terms:
-7 + x = -4.898979486

Solving
-7 + x = -4.898979486

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -4.898979486 + 7

Combine like terms: -7 + 7 = 0
0 + x = -4.898979486 + 7
x = -4.898979486 + 7

Combine like terms: -4.898979486 + 7 = 2.101020514
x = 2.101020514

Simplifying
x = 2.101020514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.898979486, 2.101020514}
Solution
x = {11.898979486, 2.101020514}

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