9(13-X)=5-4X(21-2X)+9X

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Solution for 9(13-X)=5-4X(21-2X)+9X equation: 


Simplifying
9(13 + -1X) = 5 + -4X(21 + -2X) + 9X
(13 * 9 + -1X * 9) = 5 + -4X(21 + -2X) + 9X
(117 + -9X) = 5 + -4X(21 + -2X) + 9X
117 + -9X = 5 + (21 * -4X + -2X * -4X) + 9X
117 + -9X = 5 + (-84X + 8X2) + 9X

Reorder the terms:
117 + -9X = 5 + -84X + 9X + 8X2

Combine like terms: -84X + 9X = -75X
117 + -9X = 5 + -75X + 8X2

Solving
117 + -9X = 5 + -75X + 8X2

Solving for variable 'X'.

Reorder the terms:
117 + -5 + -9X + 75X + -8X2 = 5 + -75X + 8X2 + -5 + 75X + -8X2

Combine like terms: 117 + -5 = 112
112 + -9X + 75X + -8X2 = 5 + -75X + 8X2 + -5 + 75X + -8X2

Combine like terms: -9X + 75X = 66X
112 + 66X + -8X2 = 5 + -75X + 8X2 + -5 + 75X + -8X2

Reorder the terms:
112 + 66X + -8X2 = 5 + -5 + -75X + 75X + 8X2 + -8X2

Combine like terms: 5 + -5 = 0
112 + 66X + -8X2 = 0 + -75X + 75X + 8X2 + -8X2
112 + 66X + -8X2 = -75X + 75X + 8X2 + -8X2

Combine like terms: -75X + 75X = 0
112 + 66X + -8X2 = 0 + 8X2 + -8X2
112 + 66X + -8X2 = 8X2 + -8X2

Combine like terms: 8X2 + -8X2 = 0
112 + 66X + -8X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(56 + 33X + -4X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(56 + 33X + -4X2)' equal to zero and attempt to solve:

Simplifying
56 + 33X + -4X2 = 0

Solving
56 + 33X + -4X2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-14 + -8.25X + X2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -8.25X + 14 + X2 = 0 + 14

Reorder the terms:
-14 + 14 + -8.25X + X2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -8.25X + X2 = 0 + 14
-8.25X + X2 = 0 + 14

Combine like terms: 0 + 14 = 14
-8.25X + X2 = 14

The X term is -8.25X.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25X + 17.015625 + X2 = 14 + 17.015625

Reorder the terms:
17.015625 + -8.25X + X2 = 14 + 17.015625

Combine like terms: 14 + 17.015625 = 31.015625
17.015625 + -8.25X + X2 = 31.015625

Factor a perfect square on the left side:
(X + -4.125)(X + -4.125) = 31.015625

Calculate the square root of the right side: 5.569167352

Break this problem into two subproblems by setting 
(X + -4.125) equal to 5.569167352 and -5.569167352.


Subproblem 1
X + -4.125 = 5.569167352

Simplifying
X + -4.125 = 5.569167352

Reorder the terms:
-4.125 + X = 5.569167352

Solving
-4.125 + X = 5.569167352

Solving for variable 'X'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + X = 5.569167352 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + X = 5.569167352 + 4.125
X = 5.569167352 + 4.125

Combine like terms: 5.569167352 + 4.125 = 9.694167352
X = 9.694167352

Simplifying
X = 9.694167352


Subproblem 2
X + -4.125 = -5.569167352

Simplifying
X + -4.125 = -5.569167352

Reorder the terms:
-4.125 + X = -5.569167352

Solving
-4.125 + X = -5.569167352

Solving for variable 'X'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + X = -5.569167352 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + X = -5.569167352 + 4.125
X = -5.569167352 + 4.125

Combine like terms: -5.569167352 + 4.125 = -1.444167352
X = -1.444167352

Simplifying
X = -1.444167352


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {9.694167352, -1.444167352}
Solution
X = {9.694167352, -1.444167352}

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