22x^2-19x-2=0

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Solution for 22x^2-19x-2=0 equation:


Simplifying
22x2 + -19x + -2 = 0

Reorder the terms:
-2 + -19x + 22x2 = 0

Solving
-2 + -19x + 22x2 = 0

Solving for variable 'x'.

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

Divide each side by '22'.
-0.09090909091 + -0.8636363636x + x2 = 0

Move the constant term to the right:

Add '0.09090909091' to each side of the equation.
-0.09090909091 + -0.8636363636x + 0.09090909091 + x2 = 0 + 0.09090909091

Reorder the terms:
-0.09090909091 + 0.09090909091 + -0.8636363636x + x2 = 0 + 0.09090909091

Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000
0.00000000000 + -0.8636363636x + x2 = 0 + 0.09090909091
-0.8636363636x + x2 = 0 + 0.09090909091

Combine like terms: 0 + 0.09090909091 = 0.09090909091
-0.8636363636x + x2 = 0.09090909091

The x term is -0.8636363636x.  Take half its coefficient (-0.4318181818).
Square it (0.1864669421) and add it to both sides.

Add '0.1864669421' to each side of the equation.
-0.8636363636x + 0.1864669421 + x2 = 0.09090909091 + 0.1864669421

Reorder the terms:
0.1864669421 + -0.8636363636x + x2 = 0.09090909091 + 0.1864669421

Combine like terms: 0.09090909091 + 0.1864669421 = 0.27737603301
0.1864669421 + -0.8636363636x + x2 = 0.27737603301

Factor a perfect square on the left side:
(x + -0.4318181818)(x + -0.4318181818) = 0.27737603301

Calculate the square root of the right side: 0.52666501

Break this problem into two subproblems by setting 
(x + -0.4318181818) equal to 0.52666501 and -0.52666501.

Subproblem 1

x + -0.4318181818 = 0.52666501 Simplifying x + -0.4318181818 = 0.52666501 Reorder the terms: -0.4318181818 + x = 0.52666501 Solving -0.4318181818 + x = 0.52666501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4318181818' to each side of the equation. -0.4318181818 + 0.4318181818 + x = 0.52666501 + 0.4318181818 Combine like terms: -0.4318181818 + 0.4318181818 = 0.0000000000 0.0000000000 + x = 0.52666501 + 0.4318181818 x = 0.52666501 + 0.4318181818 Combine like terms: 0.52666501 + 0.4318181818 = 0.9584831918 x = 0.9584831918 Simplifying x = 0.9584831918

Subproblem 2

x + -0.4318181818 = -0.52666501 Simplifying x + -0.4318181818 = -0.52666501 Reorder the terms: -0.4318181818 + x = -0.52666501 Solving -0.4318181818 + x = -0.52666501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4318181818' to each side of the equation. -0.4318181818 + 0.4318181818 + x = -0.52666501 + 0.4318181818 Combine like terms: -0.4318181818 + 0.4318181818 = 0.0000000000 0.0000000000 + x = -0.52666501 + 0.4318181818 x = -0.52666501 + 0.4318181818 Combine like terms: -0.52666501 + 0.4318181818 = -0.0948468282 x = -0.0948468282 Simplifying x = -0.0948468282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9584831918, -0.0948468282}

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