17x^2+21x-22=0

Solution for 17x^2+21x-22=0 equation:

Simplifying
17x2 + 21x + -22 = 0

Reorder the terms:
-22 + 21x + 17x2 = 0

Solving
-22 + 21x + 17x2 = 0

Solving for variable 'x'.

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

Divide each side by '17'.
-1.294117647 + 1.235294118x + x2 = 0

Move the constant term to the right:

Add '1.294117647' to each side of the equation.
-1.294117647 + 1.235294118x + 1.294117647 + x2 = 0 + 1.294117647

Reorder the terms:
-1.294117647 + 1.294117647 + 1.235294118x + x2 = 0 + 1.294117647

Combine like terms: -1.294117647 + 1.294117647 = 0.000000000
0.000000000 + 1.235294118x + x2 = 0 + 1.294117647
1.235294118x + x2 = 0 + 1.294117647

Combine like terms: 0 + 1.294117647 = 1.294117647
1.235294118x + x2 = 1.294117647

The x term is 1.235294118x.  Take half its coefficient (0.617647059).
Square it (0.3814878895) and add it to both sides.

Add '0.3814878895' to each side of the equation.
1.235294118x + 0.3814878895 + x2 = 1.294117647 + 0.3814878895

Reorder the terms:
0.3814878895 + 1.235294118x + x2 = 1.294117647 + 0.3814878895

Combine like terms: 1.294117647 + 0.3814878895 = 1.6756055365
0.3814878895 + 1.235294118x + x2 = 1.6756055365

Factor a perfect square on the left side:
(x + 0.617647059)(x + 0.617647059) = 1.6756055365

Calculate the square root of the right side: 1.294451829

Break this problem into two subproblems by setting 
(x + 0.617647059) equal to 1.294451829 and -1.294451829.

Subproblem 1
x + 0.617647059 = 1.294451829

Simplifying
x + 0.617647059 = 1.294451829

Reorder the terms:
0.617647059 + x = 1.294451829

Solving
0.617647059 + x = 1.294451829

Solving for variable 'x'.

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

Add '-0.617647059' to each side of the equation.
0.617647059 + -0.617647059 + x = 1.294451829 + -0.617647059

Combine like terms: 0.617647059 + -0.617647059 = 0.000000000
0.000000000 + x = 1.294451829 + -0.617647059
x = 1.294451829 + -0.617647059

Combine like terms: 1.294451829 + -0.617647059 = 0.67680477
x = 0.67680477

Simplifying
x = 0.67680477

Subproblem 2
x + 0.617647059 = -1.294451829

Simplifying
x + 0.617647059 = -1.294451829

Reorder the terms:
0.617647059 + x = -1.294451829

Solving
0.617647059 + x = -1.294451829

Solving for variable 'x'.

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

Add '-0.617647059' to each side of the equation.
0.617647059 + -0.617647059 + x = -1.294451829 + -0.617647059

Combine like terms: 0.617647059 + -0.617647059 = 0.000000000
0.000000000 + x = -1.294451829 + -0.617647059
x = -1.294451829 + -0.617647059

Combine like terms: -1.294451829 + -0.617647059 = -1.912098888
x = -1.912098888

Simplifying
x = -1.912098888

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.67680477, -1.912098888}