r^2-16r=9

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Solution for r^2-16r=9 equation:


Simplifying
r2 + -16r = 9

Reorder the terms:
-16r + r2 = 9

Solving
-16r + r2 = 9

Solving for variable 'r'.

Reorder the terms:
-9 + -16r + r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -16r + 9 + r2 = 0 + 9

Reorder the terms:
-9 + 9 + -16r + r2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -16r + r2 = 0 + 9
-16r + r2 = 0 + 9

Combine like terms: 0 + 9 = 9
-16r + r2 = 9

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 = 9 + 64

Reorder the terms:
64 + -16r + r2 = 9 + 64

Combine like terms: 9 + 64 = 73
64 + -16r + r2 = 73

Factor a perfect square on the left side:
(r + -8)(r + -8) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(r + -8) equal to 8.544003745 and -8.544003745.

Subproblem 1

r + -8 = 8.544003745 Simplifying r + -8 = 8.544003745 Reorder the terms: -8 + r = 8.544003745 Solving -8 + r = 8.544003745 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 = 8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + r = 8.544003745 + 8 r = 8.544003745 + 8 Combine like terms: 8.544003745 + 8 = 16.544003745 r = 16.544003745 Simplifying r = 16.544003745

Subproblem 2

r + -8 = -8.544003745 Simplifying r + -8 = -8.544003745 Reorder the terms: -8 + r = -8.544003745 Solving -8 + r = -8.544003745 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 = -8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + r = -8.544003745 + 8 r = -8.544003745 + 8 Combine like terms: -8.544003745 + 8 = -0.544003745 r = -0.544003745 Simplifying r = -0.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. r = {16.544003745, -0.544003745}

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