(17-2x)(22-2x)=190

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Solution for (17-2x)(22-2x)=190 equation: 


Simplifying
(17 + -2x)(22 + -2x) = 190

Multiply (17 + -2x) * (22 + -2x)
(17(22 + -2x) + -2x * (22 + -2x)) = 190
((22 * 17 + -2x * 17) + -2x * (22 + -2x)) = 190
((374 + -34x) + -2x * (22 + -2x)) = 190
(374 + -34x + (22 * -2x + -2x * -2x)) = 190
(374 + -34x + (-44x + 4x2)) = 190

Combine like terms: -34x + -44x = -78x
(374 + -78x + 4x2) = 190

Solving
374 + -78x + 4x2 = 190

Solving for variable 'x'.

Reorder the terms:
374 + -190 + -78x + 4x2 = 190 + -190

Combine like terms: 374 + -190 = 184
184 + -78x + 4x2 = 190 + -190

Combine like terms: 190 + -190 = 0
184 + -78x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(92 + -39x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(92 + -39x + 2x2)' equal to zero and attempt to solve:

Simplifying
92 + -39x + 2x2 = 0

Solving
92 + -39x + 2x2 = 0

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

Divide each side by '2'.
46 + -19.5x + x2 = 0

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -19.5x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + -19.5x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -19.5x + x2 = 0 + -46
-19.5x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
-19.5x + x2 = -46

The x term is -19.5x.  Take half its coefficient (-9.75).
Square it (95.0625) and add it to both sides.

Add '95.0625' to each side of the equation.
-19.5x + 95.0625 + x2 = -46 + 95.0625

Reorder the terms:
95.0625 + -19.5x + x2 = -46 + 95.0625

Combine like terms: -46 + 95.0625 = 49.0625
95.0625 + -19.5x + x2 = 49.0625

Factor a perfect square on the left side:
(x + -9.75)(x + -9.75) = 49.0625

Calculate the square root of the right side: 7.004462863

Break this problem into two subproblems by setting 
(x + -9.75) equal to 7.004462863 and -7.004462863.


Subproblem 1
x + -9.75 = 7.004462863

Simplifying
x + -9.75 = 7.004462863

Reorder the terms:
-9.75 + x = 7.004462863

Solving
-9.75 + x = 7.004462863

Solving for variable 'x'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + x = 7.004462863 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + x = 7.004462863 + 9.75
x = 7.004462863 + 9.75

Combine like terms: 7.004462863 + 9.75 = 16.754462863
x = 16.754462863

Simplifying
x = 16.754462863


Subproblem 2
x + -9.75 = -7.004462863

Simplifying
x + -9.75 = -7.004462863

Reorder the terms:
-9.75 + x = -7.004462863

Solving
-9.75 + x = -7.004462863

Solving for variable 'x'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + x = -7.004462863 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + x = -7.004462863 + 9.75
x = -7.004462863 + 9.75

Combine like terms: -7.004462863 + 9.75 = 2.745537137
x = 2.745537137

Simplifying
x = 2.745537137


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.754462863, 2.745537137}
Solution
x = {16.754462863, 2.745537137}

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