3x(7-2x)=22-8x

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Solution for 3x(7-2x)=22-8x equation: 


Simplifying
3x(7 + -2x) = 22 + -8x
(7 * 3x + -2x * 3x) = 22 + -8x
(21x + -6x2) = 22 + -8x

Solving
21x + -6x2 = 22 + -8x

Solving for variable 'x'.

Reorder the terms:
-22 + 21x + 8x + -6x2 = 22 + -8x + -22 + 8x

Combine like terms: 21x + 8x = 29x
-22 + 29x + -6x2 = 22 + -8x + -22 + 8x

Reorder the terms:
-22 + 29x + -6x2 = 22 + -22 + -8x + 8x

Combine like terms: 22 + -22 = 0
-22 + 29x + -6x2 = 0 + -8x + 8x
-22 + 29x + -6x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-22 + 29x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
3.666666667 + -4.833333333x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -4.833333333x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -4.833333333x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -4.833333333x + x2 = 0 + -3.666666667
-4.833333333x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-4.833333333x + x2 = -3.666666667

The x term is -4.833333333x.  Take half its coefficient (-2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
-4.833333333x + 5.840277779 + x2 = -3.666666667 + 5.840277779

Reorder the terms:
5.840277779 + -4.833333333x + x2 = -3.666666667 + 5.840277779

Combine like terms: -3.666666667 + 5.840277779 = 2.173611112
5.840277779 + -4.833333333x + x2 = 2.173611112

Factor a perfect square on the left side:
(x + -2.416666667)(x + -2.416666667) = 2.173611112

Calculate the square root of the right side: 1.474317168

Break this problem into two subproblems by setting 
(x + -2.416666667) equal to 1.474317168 and -1.474317168.


Subproblem 1
x + -2.416666667 = 1.474317168

Simplifying
x + -2.416666667 = 1.474317168

Reorder the terms:
-2.416666667 + x = 1.474317168

Solving
-2.416666667 + x = 1.474317168

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = 1.474317168 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = 1.474317168 + 2.416666667
x = 1.474317168 + 2.416666667

Combine like terms: 1.474317168 + 2.416666667 = 3.890983835
x = 3.890983835

Simplifying
x = 3.890983835


Subproblem 2
x + -2.416666667 = -1.474317168

Simplifying
x + -2.416666667 = -1.474317168

Reorder the terms:
-2.416666667 + x = -1.474317168

Solving
-2.416666667 + x = -1.474317168

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = -1.474317168 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = -1.474317168 + 2.416666667
x = -1.474317168 + 2.416666667

Combine like terms: -1.474317168 + 2.416666667 = 0.942349499
x = 0.942349499

Simplifying
x = 0.942349499


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.890983835, 0.942349499}

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