4x^2+22x-1=0

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Solution for 4x^2+22x-1=0 equation: 


Simplifying
4x2 + 22x + -1 = 0

Reorder the terms:
-1 + 22x + 4x2 = 0

Solving
-1 + 22x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-0.25 + 5.5x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 5.5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 5.5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 5.5x + x2 = 0 + 0.25
5.5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
5.5x + x2 = 0.25

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 = 0.25 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 0.25 + 7.5625

Combine like terms: 0.25 + 7.5625 = 7.8125
7.5625 + 5.5x + x2 = 7.8125

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 7.8125

Calculate the square root of the right side: 2.795084972

Break this problem into two subproblems by setting 
(x + 2.75) equal to 2.795084972 and -2.795084972.


Subproblem 1
x + 2.75 = 2.795084972

Simplifying
x + 2.75 = 2.795084972

Reorder the terms:
2.75 + x = 2.795084972

Solving
2.75 + x = 2.795084972

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 = 2.795084972 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 2.795084972 + -2.75
x = 2.795084972 + -2.75

Combine like terms: 2.795084972 + -2.75 = 0.045084972
x = 0.045084972

Simplifying
x = 0.045084972


Subproblem 2
x + 2.75 = -2.795084972

Simplifying
x + 2.75 = -2.795084972

Reorder the terms:
2.75 + x = -2.795084972

Solving
2.75 + x = -2.795084972

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 = -2.795084972 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -2.795084972 + -2.75
x = -2.795084972 + -2.75

Combine like terms: -2.795084972 + -2.75 = -5.545084972
x = -5.545084972

Simplifying
x = -5.545084972


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.045084972, -5.545084972}

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