15x^2-4x-22=0

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Solution for 15x^2-4x-22=0 equation: 


Simplifying
15x2 + -4x + -22 = 0

Reorder the terms:
-22 + -4x + 15x2 = 0

Solving
-22 + -4x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-1.466666667 + -0.2666666667x + x2 = 0

Move the constant term to the right:

Add '1.466666667' to each side of the equation.
-1.466666667 + -0.2666666667x + 1.466666667 + x2 = 0 + 1.466666667

Reorder the terms:
-1.466666667 + 1.466666667 + -0.2666666667x + x2 = 0 + 1.466666667

Combine like terms: -1.466666667 + 1.466666667 = 0.000000000
0.000000000 + -0.2666666667x + x2 = 0 + 1.466666667
-0.2666666667x + x2 = 0 + 1.466666667

Combine like terms: 0 + 1.466666667 = 1.466666667
-0.2666666667x + x2 = 1.466666667

The x term is -0.2666666667x.  Take half its coefficient (-0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
-0.2666666667x + 0.01777777780 + x2 = 1.466666667 + 0.01777777780

Reorder the terms:
0.01777777780 + -0.2666666667x + x2 = 1.466666667 + 0.01777777780

Combine like terms: 1.466666667 + 0.01777777780 = 1.4844444448
0.01777777780 + -0.2666666667x + x2 = 1.4844444448

Factor a perfect square on the left side:
(x + -0.1333333334)(x + -0.1333333334) = 1.4844444448

Calculate the square root of the right side: 1.218377792

Break this problem into two subproblems by setting 
(x + -0.1333333334) equal to 1.218377792 and -1.218377792.


Subproblem 1
x + -0.1333333334 = 1.218377792

Simplifying
x + -0.1333333334 = 1.218377792

Reorder the terms:
-0.1333333334 + x = 1.218377792

Solving
-0.1333333334 + x = 1.218377792

Solving for variable 'x'.

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

Add '0.1333333334' to each side of the equation.
-0.1333333334 + 0.1333333334 + x = 1.218377792 + 0.1333333334

Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000
0.0000000000 + x = 1.218377792 + 0.1333333334
x = 1.218377792 + 0.1333333334

Combine like terms: 1.218377792 + 0.1333333334 = 1.3517111254
x = 1.3517111254

Simplifying
x = 1.3517111254


Subproblem 2
x + -0.1333333334 = -1.218377792

Simplifying
x + -0.1333333334 = -1.218377792

Reorder the terms:
-0.1333333334 + x = -1.218377792

Solving
-0.1333333334 + x = -1.218377792

Solving for variable 'x'.

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

Add '0.1333333334' to each side of the equation.
-0.1333333334 + 0.1333333334 + x = -1.218377792 + 0.1333333334

Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000
0.0000000000 + x = -1.218377792 + 0.1333333334
x = -1.218377792 + 0.1333333334

Combine like terms: -1.218377792 + 0.1333333334 = -1.0850444586
x = -1.0850444586

Simplifying
x = -1.0850444586


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3517111254, -1.0850444586}

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