4x^2-22x-4=0

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


Simplifying
4x2 + -22x + -4 = 0

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

Solving
-4 + -22x + 4x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
-2 + -11x + 2x2 = 0

Solving
-2 + -11x + 2x2 = 0

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

Divide each side by '2'.
-1 + -5.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -5.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5.5x + x2 = 0 + 1
-5.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5.5x + x2 = 1

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 1 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 1 + 7.5625

Combine like terms: 1 + 7.5625 = 8.5625
7.5625 + -5.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.926174978 and -2.926174978.


Subproblem 1
x + -2.75 = 2.926174978

Simplifying
x + -2.75 = 2.926174978

Reorder the terms:
-2.75 + x = 2.926174978

Solving
-2.75 + x = 2.926174978

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 2.926174978 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.926174978 + 2.75
x = 2.926174978 + 2.75

Combine like terms: 2.926174978 + 2.75 = 5.676174978
x = 5.676174978

Simplifying
x = 5.676174978


Subproblem 2
x + -2.75 = -2.926174978

Simplifying
x + -2.75 = -2.926174978

Reorder the terms:
-2.75 + x = -2.926174978

Solving
-2.75 + x = -2.926174978

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -2.926174978 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.926174978 + 2.75
x = -2.926174978 + 2.75

Combine like terms: -2.926174978 + 2.75 = -0.176174978
x = -0.176174978

Simplifying
x = -0.176174978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.676174978, -0.176174978}
Solution
x = {5.676174978, -0.176174978}

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