4x^2-50x+22=0

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Solution for 4x^2-50x+22=0 equation: 


Simplifying
4x2 + -50x + 22 = 0

Reorder the terms:
22 + -50x + 4x2 = 0

Solving
22 + -50x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -25x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -25x + 2x2)' equal to zero and attempt to solve:

Simplifying
11 + -25x + 2x2 = 0

Solving
11 + -25x + 2x2 = 0

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

Divide each side by '2'.
5.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -12.5x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -12.5x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -12.5x + x2 = 0 + -5.5
-12.5x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-12.5x + x2 = -5.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -5.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -5.5 + 39.0625

Combine like terms: -5.5 + 39.0625 = 33.5625
39.0625 + -12.5x + x2 = 33.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 33.5625

Calculate the square root of the right side: 5.793315113

Break this problem into two subproblems by setting 
(x + -6.25) equal to 5.793315113 and -5.793315113.


Subproblem 1
x + -6.25 = 5.793315113

Simplifying
x + -6.25 = 5.793315113

Reorder the terms:
-6.25 + x = 5.793315113

Solving
-6.25 + x = 5.793315113

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 5.793315113 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 5.793315113 + 6.25
x = 5.793315113 + 6.25

Combine like terms: 5.793315113 + 6.25 = 12.043315113
x = 12.043315113

Simplifying
x = 12.043315113


Subproblem 2
x + -6.25 = -5.793315113

Simplifying
x + -6.25 = -5.793315113

Reorder the terms:
-6.25 + x = -5.793315113

Solving
-6.25 + x = -5.793315113

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -5.793315113 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -5.793315113 + 6.25
x = -5.793315113 + 6.25

Combine like terms: -5.793315113 + 6.25 = 0.456684887
x = 0.456684887

Simplifying
x = 0.456684887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.043315113, 0.456684887}
Solution
x = {12.043315113, 0.456684887}

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