81+r^2=(3+r)2

Solution for 81+r^2=(3+r)2 equation:

Simplifying
81 + r2 = (3 + r) * 2

Reorder the terms for easier multiplication:
81 + r2 = 2(3 + r)
81 + r2 = (3 * 2 + r * 2)
81 + r2 = (6 + 2r)

Solving
81 + r2 = 6 + 2r

Solving for variable 'r'.

Reorder the terms:
81 + -6 + -2r + r2 = 6 + 2r + -6 + -2r

Combine like terms: 81 + -6 = 75
75 + -2r + r2 = 6 + 2r + -6 + -2r

Reorder the terms:
75 + -2r + r2 = 6 + -6 + 2r + -2r

Combine like terms: 6 + -6 = 0
75 + -2r + r2 = 0 + 2r + -2r
75 + -2r + r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
75 + -2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + -2r + -75 + r2 = 0 + -75

Reorder the terms:
75 + -75 + -2r + r2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -2r + r2 = 0 + -75
-2r + r2 = 0 + -75

Combine like terms: 0 + -75 = -75
-2r + r2 = -75

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = -75 + 1

Reorder the terms:
1 + -2r + r2 = -75 + 1

Combine like terms: -75 + 1 = -74
1 + -2r + r2 = -74

Factor a perfect square on the left side:
(r + -1)(r + -1) = -74

Can't calculate square root of the right side.

The solution to this equation could not be determined.