2(292+-81x+2x*2x)=0

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Solution for 2(292+-81x+2x*2x)=0 equation: 


Simplifying
2(292 + -81x + 2x * 2x) = 0

Reorder the terms for easier multiplication:
2(292 + -81x + 2 * 2x * x) = 0

Multiply 2 * 2
2(292 + -81x + 4x * x) = 0

Multiply x * x
2(292 + -81x + 4x2) = 0
(292 * 2 + -81x * 2 + 4x2 * 2) = 0
(584 + -162x + 8x2) = 0

Solving
584 + -162x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(292 + -81x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(292 + -81x + 4x2)' equal to zero and attempt to solve:

Simplifying
292 + -81x + 4x2 = 0

Solving
292 + -81x + 4x2 = 0

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

Divide each side by '4'.
73 + -20.25x + x2 = 0

Move the constant term to the right:

Add '-73' to each side of the equation.
73 + -20.25x + -73 + x2 = 0 + -73

Reorder the terms:
73 + -73 + -20.25x + x2 = 0 + -73

Combine like terms: 73 + -73 = 0
0 + -20.25x + x2 = 0 + -73
-20.25x + x2 = 0 + -73

Combine like terms: 0 + -73 = -73
-20.25x + x2 = -73

The x term is -20.25x.  Take half its coefficient (-10.125).
Square it (102.515625) and add it to both sides.

Add '102.515625' to each side of the equation.
-20.25x + 102.515625 + x2 = -73 + 102.515625

Reorder the terms:
102.515625 + -20.25x + x2 = -73 + 102.515625

Combine like terms: -73 + 102.515625 = 29.515625
102.515625 + -20.25x + x2 = 29.515625

Factor a perfect square on the left side:
(x + -10.125)(x + -10.125) = 29.515625

Calculate the square root of the right side: 5.432828453

Break this problem into two subproblems by setting 
(x + -10.125) equal to 5.432828453 and -5.432828453.


Subproblem 1
x + -10.125 = 5.432828453

Simplifying
x + -10.125 = 5.432828453

Reorder the terms:
-10.125 + x = 5.432828453

Solving
-10.125 + x = 5.432828453

Solving for variable 'x'.

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

Add '10.125' to each side of the equation.
-10.125 + 10.125 + x = 5.432828453 + 10.125

Combine like terms: -10.125 + 10.125 = 0.000
0.000 + x = 5.432828453 + 10.125
x = 5.432828453 + 10.125

Combine like terms: 5.432828453 + 10.125 = 15.557828453
x = 15.557828453

Simplifying
x = 15.557828453


Subproblem 2
x + -10.125 = -5.432828453

Simplifying
x + -10.125 = -5.432828453

Reorder the terms:
-10.125 + x = -5.432828453

Solving
-10.125 + x = -5.432828453

Solving for variable 'x'.

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

Add '10.125' to each side of the equation.
-10.125 + 10.125 + x = -5.432828453 + 10.125

Combine like terms: -10.125 + 10.125 = 0.000
0.000 + x = -5.432828453 + 10.125
x = -5.432828453 + 10.125

Combine like terms: -5.432828453 + 10.125 = 4.692171547
x = 4.692171547

Simplifying
x = 4.692171547


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.557828453, 4.692171547}
Solution
x = {15.557828453, 4.692171547}

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