22-5x(38-4x)=12

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Solution for 22-5x(38-4x)=12 equation: 


Simplifying
22 + -5x(38 + -4x) = 12
22 + (38 * -5x + -4x * -5x) = 12
22 + (-190x + 20x2) = 12

Solving
22 + -190x + 20x2 = 12

Solving for variable 'x'.

Reorder the terms:
22 + -12 + -190x + 20x2 = 12 + -12

Combine like terms: 22 + -12 = 10
10 + -190x + 20x2 = 12 + -12

Combine like terms: 12 + -12 = 0
10 + -190x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -19x + 2x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(1 + -19x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -19x + 2x2 = 0

Solving
1 + -19x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -9.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -9.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -9.5x + x2 = 0 + -0.5
-9.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-9.5x + x2 = -0.5

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = -0.5 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -0.5 + 22.5625

Combine like terms: -0.5 + 22.5625 = 22.0625
22.5625 + -9.5x + x2 = 22.0625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 22.0625

Calculate the square root of the right side: 4.697073557

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.697073557 and -4.697073557.


Subproblem 1
x + -4.75 = 4.697073557

Simplifying
x + -4.75 = 4.697073557

Reorder the terms:
-4.75 + x = 4.697073557

Solving
-4.75 + x = 4.697073557

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 4.697073557 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 4.697073557 + 4.75
x = 4.697073557 + 4.75

Combine like terms: 4.697073557 + 4.75 = 9.447073557
x = 9.447073557

Simplifying
x = 9.447073557


Subproblem 2
x + -4.75 = -4.697073557

Simplifying
x + -4.75 = -4.697073557

Reorder the terms:
-4.75 + x = -4.697073557

Solving
-4.75 + x = -4.697073557

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -4.697073557 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -4.697073557 + 4.75
x = -4.697073557 + 4.75

Combine like terms: -4.697073557 + 4.75 = 0.052926443
x = 0.052926443

Simplifying
x = 0.052926443


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.447073557, 0.052926443}
Solution
x = {9.447073557, 0.052926443}

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