2r^2+5r-17=2

Solution for 2r^2+5r-17=2 equation:

Simplifying
2r2 + 5r + -17 = 2

Reorder the terms:
-17 + 5r + 2r2 = 2

Solving
-17 + 5r + 2r2 = 2

Solving for variable 'r'.

Reorder the terms:
-17 + -2 + 5r + 2r2 = 2 + -2

Combine like terms: -17 + -2 = -19
-19 + 5r + 2r2 = 2 + -2

Combine like terms: 2 + -2 = 0
-19 + 5r + 2r2 = 0

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

Divide each side by '2'.
-9.5 + 2.5r + r2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 2.5r + 9.5 + r2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 2.5r + r2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 2.5r + r2 = 0 + 9.5
2.5r + r2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
2.5r + r2 = 9.5

The r term is 2.5r.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5r + 1.5625 + r2 = 9.5 + 1.5625

Reorder the terms:
1.5625 + 2.5r + r2 = 9.5 + 1.5625

Combine like terms: 9.5 + 1.5625 = 11.0625
1.5625 + 2.5r + r2 = 11.0625

Factor a perfect square on the left side:
(r + 1.25)(r + 1.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(r + 1.25) equal to 3.326033674 and -3.326033674.

Subproblem 1
r + 1.25 = 3.326033674

Simplifying
r + 1.25 = 3.326033674

Reorder the terms:
1.25 + r = 3.326033674

Solving
1.25 + r = 3.326033674

Solving for variable 'r'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + r = 3.326033674 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + r = 3.326033674 + -1.25
r = 3.326033674 + -1.25

Combine like terms: 3.326033674 + -1.25 = 2.076033674
r = 2.076033674

Simplifying
r = 2.076033674

Subproblem 2
r + 1.25 = -3.326033674

Simplifying
r + 1.25 = -3.326033674

Reorder the terms:
1.25 + r = -3.326033674

Solving
1.25 + r = -3.326033674

Solving for variable 'r'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + r = -3.326033674 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + r = -3.326033674 + -1.25
r = -3.326033674 + -1.25

Combine like terms: -3.326033674 + -1.25 = -4.576033674
r = -4.576033674

Simplifying
r = -4.576033674

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.076033674, -4.576033674}