-17x+32=11x^2-17

Solution for -17x+32=11x^2-17 equation:

Simplifying
-17x + 32 = 11x2 + -17

Reorder the terms:
32 + -17x = 11x2 + -17

Reorder the terms:
32 + -17x = -17 + 11x2

Solving
32 + -17x = -17 + 11x2

Solving for variable 'x'.

Reorder the terms:
32 + 17 + -17x + -11x2 = -17 + 11x2 + 17 + -11x2

Combine like terms: 32 + 17 = 49
49 + -17x + -11x2 = -17 + 11x2 + 17 + -11x2

Reorder the terms:
49 + -17x + -11x2 = -17 + 17 + 11x2 + -11x2

Combine like terms: -17 + 17 = 0
49 + -17x + -11x2 = 0 + 11x2 + -11x2
49 + -17x + -11x2 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
49 + -17x + -11x2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
-4.454545455 + 1.545454545x + x2 = 0

Move the constant term to the right:

Add '4.454545455' to each side of the equation.
-4.454545455 + 1.545454545x + 4.454545455 + x2 = 0 + 4.454545455

Reorder the terms:
-4.454545455 + 4.454545455 + 1.545454545x + x2 = 0 + 4.454545455

Combine like terms: -4.454545455 + 4.454545455 = 0.000000000
0.000000000 + 1.545454545x + x2 = 0 + 4.454545455
1.545454545x + x2 = 0 + 4.454545455

Combine like terms: 0 + 4.454545455 = 4.454545455
1.545454545x + x2 = 4.454545455

The x term is 1.545454545x.  Take half its coefficient (0.7727272725).
Square it (0.5971074377) and add it to both sides.

Add '0.5971074377' to each side of the equation.
1.545454545x + 0.5971074377 + x2 = 4.454545455 + 0.5971074377

Reorder the terms:
0.5971074377 + 1.545454545x + x2 = 4.454545455 + 0.5971074377

Combine like terms: 4.454545455 + 0.5971074377 = 5.0516528927
0.5971074377 + 1.545454545x + x2 = 5.0516528927

Factor a perfect square on the left side:
(x + 0.7727272725)(x + 0.7727272725) = 5.0516528927

Calculate the square root of the right side: 2.247588239

Break this problem into two subproblems by setting 
(x + 0.7727272725) equal to 2.247588239 and -2.247588239.

Subproblem 1
x + 0.7727272725 = 2.247588239

Simplifying
x + 0.7727272725 = 2.247588239

Reorder the terms:
0.7727272725 + x = 2.247588239

Solving
0.7727272725 + x = 2.247588239

Solving for variable 'x'.

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

Add '-0.7727272725' to each side of the equation.
0.7727272725 + -0.7727272725 + x = 2.247588239 + -0.7727272725

Combine like terms: 0.7727272725 + -0.7727272725 = 0.0000000000
0.0000000000 + x = 2.247588239 + -0.7727272725
x = 2.247588239 + -0.7727272725

Combine like terms: 2.247588239 + -0.7727272725 = 1.4748609665
x = 1.4748609665

Simplifying
x = 1.4748609665

Subproblem 2
x + 0.7727272725 = -2.247588239

Simplifying
x + 0.7727272725 = -2.247588239

Reorder the terms:
0.7727272725 + x = -2.247588239

Solving
0.7727272725 + x = -2.247588239

Solving for variable 'x'.

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

Add '-0.7727272725' to each side of the equation.
0.7727272725 + -0.7727272725 + x = -2.247588239 + -0.7727272725

Combine like terms: 0.7727272725 + -0.7727272725 = 0.0000000000
0.0000000000 + x = -2.247588239 + -0.7727272725
x = -2.247588239 + -0.7727272725

Combine like terms: -2.247588239 + -0.7727272725 = -3.0203155115
x = -3.0203155115

Simplifying
x = -3.0203155115

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4748609665, -3.0203155115}