4x^2-22x-3=0

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Solution for 4x^2-22x-3=0 equation: 


Simplifying
4x2 + -22x + -3 = 0

Reorder the terms:
-3 + -22x + 4x2 = 0

Solving
-3 + -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'.
-0.75 + -5.5x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -5.5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -5.5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -5.5x + x2 = 0 + 0.75
-5.5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-5.5x + x2 = 0.75

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 = 0.75 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 0.75 + 7.5625

Combine like terms: 0.75 + 7.5625 = 8.3125
7.5625 + -5.5x + x2 = 8.3125

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 8.3125

Calculate the square root of the right side: 2.883140649

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.883140649 and -2.883140649.


Subproblem 1
x + -2.75 = 2.883140649

Simplifying
x + -2.75 = 2.883140649

Reorder the terms:
-2.75 + x = 2.883140649

Solving
-2.75 + x = 2.883140649

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 = 2.883140649 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.883140649 + 2.75
x = 2.883140649 + 2.75

Combine like terms: 2.883140649 + 2.75 = 5.633140649
x = 5.633140649

Simplifying
x = 5.633140649


Subproblem 2
x + -2.75 = -2.883140649

Simplifying
x + -2.75 = -2.883140649

Reorder the terms:
-2.75 + x = -2.883140649

Solving
-2.75 + x = -2.883140649

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 = -2.883140649 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.883140649 + 2.75
x = -2.883140649 + 2.75

Combine like terms: -2.883140649 + 2.75 = -0.133140649
x = -0.133140649

Simplifying
x = -0.133140649


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.633140649, -0.133140649}

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