(180-18x)8x+24=114

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Solution for (180-18x)8x+24=114 equation: 


Simplifying
(180 + -18x) * 8x + 24 = 114

Reorder the terms for easier multiplication:
8x(180 + -18x) + 24 = 114
(180 * 8x + -18x * 8x) + 24 = 114
(1440x + -144x2) + 24 = 114

Reorder the terms:
24 + 1440x + -144x2 = 114

Solving
24 + 1440x + -144x2 = 114

Solving for variable 'x'.

Reorder the terms:
24 + -114 + 1440x + -144x2 = 114 + -114

Combine like terms: 24 + -114 = -90
-90 + 1440x + -144x2 = 114 + -114

Combine like terms: 114 + -114 = 0
-90 + 1440x + -144x2 = 0

Factor out the Greatest Common Factor (GCF), '18'.
18(-5 + 80x + -8x2) = 0

Ignore the factor 18.

Subproblem 1
Set the factor '(-5 + 80x + -8x2)' equal to zero and attempt to solve:

Simplifying
-5 + 80x + -8x2 = 0

Solving
-5 + 80x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.625 + -10x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -10x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -10x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -10x + x2 = 0 + -0.625
-10x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-10x + x2 = -0.625

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -0.625 + 25

Reorder the terms:
25 + -10x + x2 = -0.625 + 25

Combine like terms: -0.625 + 25 = 24.375
25 + -10x + x2 = 24.375

Factor a perfect square on the left side:
(x + -5)(x + -5) = 24.375

Calculate the square root of the right side: 4.937104415

Break this problem into two subproblems by setting 
(x + -5) equal to 4.937104415 and -4.937104415.


Subproblem 1
x + -5 = 4.937104415

Simplifying
x + -5 = 4.937104415

Reorder the terms:
-5 + x = 4.937104415

Solving
-5 + x = 4.937104415

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.937104415 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.937104415 + 5
x = 4.937104415 + 5

Combine like terms: 4.937104415 + 5 = 9.937104415
x = 9.937104415

Simplifying
x = 9.937104415


Subproblem 2
x + -5 = -4.937104415

Simplifying
x + -5 = -4.937104415

Reorder the terms:
-5 + x = -4.937104415

Solving
-5 + x = -4.937104415

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.937104415 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.937104415 + 5
x = -4.937104415 + 5

Combine like terms: -4.937104415 + 5 = 0.062895585
x = 0.062895585

Simplifying
x = 0.062895585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.937104415, 0.062895585}
Solution
x = {9.937104415, 0.062895585}

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