4x+8x(900-x)=1056

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Solution for 4x+8x(900-x)=1056 equation: 


Simplifying
4x + 8x(900 + -1x) = 1056
4x + (900 * 8x + -1x * 8x) = 1056
4x + (7200x + -8x2) = 1056

Combine like terms: 4x + 7200x = 7204x
7204x + -8x2 = 1056

Solving
7204x + -8x2 = 1056

Solving for variable 'x'.

Reorder the terms:
-1056 + 7204x + -8x2 = 1056 + -1056

Combine like terms: 1056 + -1056 = 0
-1056 + 7204x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-264 + 1801x + -2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-264 + 1801x + -2x2)' equal to zero and attempt to solve:

Simplifying
-264 + 1801x + -2x2 = 0

Solving
-264 + 1801x + -2x2 = 0

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

Divide each side by '-2'.
132 + -900.5x + x2 = 0

Move the constant term to the right:

Add '-132' to each side of the equation.
132 + -900.5x + -132 + x2 = 0 + -132

Reorder the terms:
132 + -132 + -900.5x + x2 = 0 + -132

Combine like terms: 132 + -132 = 0
0 + -900.5x + x2 = 0 + -132
-900.5x + x2 = 0 + -132

Combine like terms: 0 + -132 = -132
-900.5x + x2 = -132

The x term is -900.5x.  Take half its coefficient (-450.25).
Square it (202725.0625) and add it to both sides.

Add '202725.0625' to each side of the equation.
-900.5x + 202725.0625 + x2 = -132 + 202725.0625

Reorder the terms:
202725.0625 + -900.5x + x2 = -132 + 202725.0625

Combine like terms: -132 + 202725.0625 = 202593.0625
202725.0625 + -900.5x + x2 = 202593.0625

Factor a perfect square on the left side:
(x + -450.25)(x + -450.25) = 202593.0625

Calculate the square root of the right side: 450.1033909

Break this problem into two subproblems by setting 
(x + -450.25) equal to 450.1033909 and -450.1033909.


Subproblem 1
x + -450.25 = 450.1033909

Simplifying
x + -450.25 = 450.1033909

Reorder the terms:
-450.25 + x = 450.1033909

Solving
-450.25 + x = 450.1033909

Solving for variable 'x'.

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

Add '450.25' to each side of the equation.
-450.25 + 450.25 + x = 450.1033909 + 450.25

Combine like terms: -450.25 + 450.25 = 0.00
0.00 + x = 450.1033909 + 450.25
x = 450.1033909 + 450.25

Combine like terms: 450.1033909 + 450.25 = 900.3533909
x = 900.3533909

Simplifying
x = 900.3533909


Subproblem 2
x + -450.25 = -450.1033909

Simplifying
x + -450.25 = -450.1033909

Reorder the terms:
-450.25 + x = -450.1033909

Solving
-450.25 + x = -450.1033909

Solving for variable 'x'.

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

Add '450.25' to each side of the equation.
-450.25 + 450.25 + x = -450.1033909 + 450.25

Combine like terms: -450.25 + 450.25 = 0.00
0.00 + x = -450.1033909 + 450.25
x = -450.1033909 + 450.25

Combine like terms: -450.1033909 + 450.25 = 0.1466091
x = 0.1466091

Simplifying
x = 0.1466091


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {900.3533909, 0.1466091}
Solution
x = {900.3533909, 0.1466091}

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