15x^2+21x-22=0

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Solution for 15x^2+21x-22=0 equation: 


Simplifying
15x2 + 21x + -22 = 0

Reorder the terms:
-22 + 21x + 15x2 = 0

Solving
-22 + 21x + 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 + 1.4x + x2 = 0

Move the constant term to the right:

Add '1.466666667' to each side of the equation.
-1.466666667 + 1.4x + 1.466666667 + x2 = 0 + 1.466666667

Reorder the terms:
-1.466666667 + 1.466666667 + 1.4x + x2 = 0 + 1.466666667

Combine like terms: -1.466666667 + 1.466666667 = 0.000000000
0.000000000 + 1.4x + x2 = 0 + 1.466666667
1.4x + x2 = 0 + 1.466666667

Combine like terms: 0 + 1.466666667 = 1.466666667
1.4x + x2 = 1.466666667

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 1.466666667 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 1.466666667 + 0.49

Combine like terms: 1.466666667 + 0.49 = 1.956666667
0.49 + 1.4x + x2 = 1.956666667

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 1.956666667

Calculate the square root of the right side: 1.398809017

Break this problem into two subproblems by setting 
(x + 0.7) equal to 1.398809017 and -1.398809017.


Subproblem 1
x + 0.7 = 1.398809017

Simplifying
x + 0.7 = 1.398809017

Reorder the terms:
0.7 + x = 1.398809017

Solving
0.7 + x = 1.398809017

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = 1.398809017 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 1.398809017 + -0.7
x = 1.398809017 + -0.7

Combine like terms: 1.398809017 + -0.7 = 0.698809017
x = 0.698809017

Simplifying
x = 0.698809017


Subproblem 2
x + 0.7 = -1.398809017

Simplifying
x + 0.7 = -1.398809017

Reorder the terms:
0.7 + x = -1.398809017

Solving
0.7 + x = -1.398809017

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = -1.398809017 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -1.398809017 + -0.7
x = -1.398809017 + -0.7

Combine like terms: -1.398809017 + -0.7 = -2.098809017
x = -2.098809017

Simplifying
x = -2.098809017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.698809017, -2.098809017}

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