r^2=16r+5

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Solution for r^2=16r+5 equation:


Simplifying
r2 = 16r + 5

Reorder the terms:
r2 = 5 + 16r

Solving
r2 = 5 + 16r

Solving for variable 'r'.

Reorder the terms:
-5 + -16r + r2 = 5 + 16r + -5 + -16r

Reorder the terms:
-5 + -16r + r2 = 5 + -5 + 16r + -16r

Combine like terms: 5 + -5 = 0
-5 + -16r + r2 = 0 + 16r + -16r
-5 + -16r + r2 = 16r + -16r

Combine like terms: 16r + -16r = 0
-5 + -16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -16r + 5 + r2 = 0 + 5

Reorder the terms:
-5 + 5 + -16r + r2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -16r + r2 = 0 + 5
-16r + r2 = 0 + 5

Combine like terms: 0 + 5 = 5
-16r + r2 = 5

The r term is -16r.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16r + 64 + r2 = 5 + 64

Reorder the terms:
64 + -16r + r2 = 5 + 64

Combine like terms: 5 + 64 = 69
64 + -16r + r2 = 69

Factor a perfect square on the left side:
(r + -8)(r + -8) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(r + -8) equal to 8.306623863 and -8.306623863.

Subproblem 1

r + -8 = 8.306623863 Simplifying r + -8 = 8.306623863 Reorder the terms: -8 + r = 8.306623863 Solving -8 + r = 8.306623863 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = 8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + r = 8.306623863 + 8 r = 8.306623863 + 8 Combine like terms: 8.306623863 + 8 = 16.306623863 r = 16.306623863 Simplifying r = 16.306623863

Subproblem 2

r + -8 = -8.306623863 Simplifying r + -8 = -8.306623863 Reorder the terms: -8 + r = -8.306623863 Solving -8 + r = -8.306623863 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = -8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + r = -8.306623863 + 8 r = -8.306623863 + 8 Combine like terms: -8.306623863 + 8 = -0.306623863 r = -0.306623863 Simplifying r = -0.306623863

Solution

The solution to the problem is based on the solutions from the subproblems. r = {16.306623863, -0.306623863}

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