4x^2-92x+440=0

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Solution for 4x^2-92x+440=0 equation: 


Simplifying
4x2 + -92x + 440 = 0

Reorder the terms:
440 + -92x + 4x2 = 0

Solving
440 + -92x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(110 + -23x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(110 + -23x + x2)' equal to zero and attempt to solve:

Simplifying
110 + -23x + x2 = 0

Solving
110 + -23x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-110' to each side of the equation.
110 + -23x + -110 + x2 = 0 + -110

Reorder the terms:
110 + -110 + -23x + x2 = 0 + -110

Combine like terms: 110 + -110 = 0
0 + -23x + x2 = 0 + -110
-23x + x2 = 0 + -110

Combine like terms: 0 + -110 = -110
-23x + x2 = -110

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -110 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -110 + 132.25

Combine like terms: -110 + 132.25 = 22.25
132.25 + -23x + x2 = 22.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -11.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + -11.5 = 4.716990566

Simplifying
x + -11.5 = 4.716990566

Reorder the terms:
-11.5 + x = 4.716990566

Solving
-11.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 4.716990566 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 4.716990566 + 11.5
x = 4.716990566 + 11.5

Combine like terms: 4.716990566 + 11.5 = 16.216990566
x = 16.216990566

Simplifying
x = 16.216990566


Subproblem 2
x + -11.5 = -4.716990566

Simplifying
x + -11.5 = -4.716990566

Reorder the terms:
-11.5 + x = -4.716990566

Solving
-11.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -4.716990566 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -4.716990566 + 11.5
x = -4.716990566 + 11.5

Combine like terms: -4.716990566 + 11.5 = 6.783009434
x = 6.783009434

Simplifying
x = 6.783009434


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.216990566, 6.783009434}
Solution
x = {16.216990566, 6.783009434}

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