9r^2-5r-10=5

Solution for 9r^2-5r-10=5 equation:

Simplifying
9r2 + -5r + -10 = 5

Reorder the terms:
-10 + -5r + 9r2 = 5

Solving
-10 + -5r + 9r2 = 5

Solving for variable 'r'.

Reorder the terms:
-10 + -5 + -5r + 9r2 = 5 + -5

Combine like terms: -10 + -5 = -15
-15 + -5r + 9r2 = 5 + -5

Combine like terms: 5 + -5 = 0
-15 + -5r + 9r2 = 0

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

Divide each side by '9'.
-1.666666667 + -0.5555555556r + r2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -0.5555555556r + 1.666666667 + r2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -0.5555555556r + r2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -0.5555555556r + r2 = 0 + 1.666666667
-0.5555555556r + r2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-0.5555555556r + r2 = 1.666666667

The r term is -0.5555555556r.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556r + 0.07716049384 + r2 = 1.666666667 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556r + r2 = 1.666666667 + 0.07716049384

Combine like terms: 1.666666667 + 0.07716049384 = 1.74382716084
0.07716049384 + -0.5555555556r + r2 = 1.74382716084

Factor a perfect square on the left side:
(r + -0.2777777778)(r + -0.2777777778) = 1.74382716084

Calculate the square root of the right side: 1.320540481

Break this problem into two subproblems by setting 
(r + -0.2777777778) equal to 1.320540481 and -1.320540481.

Subproblem 1
r + -0.2777777778 = 1.320540481

Simplifying
r + -0.2777777778 = 1.320540481

Reorder the terms:
-0.2777777778 + r = 1.320540481

Solving
-0.2777777778 + r = 1.320540481

Solving for variable 'r'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + r = 1.320540481 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + r = 1.320540481 + 0.2777777778
r = 1.320540481 + 0.2777777778

Combine like terms: 1.320540481 + 0.2777777778 = 1.5983182588
r = 1.5983182588

Simplifying
r = 1.5983182588

Subproblem 2
r + -0.2777777778 = -1.320540481

Simplifying
r + -0.2777777778 = -1.320540481

Reorder the terms:
-0.2777777778 + r = -1.320540481

Solving
-0.2777777778 + r = -1.320540481

Solving for variable 'r'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + r = -1.320540481 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + r = -1.320540481 + 0.2777777778
r = -1.320540481 + 0.2777777778

Combine like terms: -1.320540481 + 0.2777777778 = -1.0427627032
r = -1.0427627032

Simplifying
r = -1.0427627032

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.5983182588, -1.0427627032}