r^2-4r=16

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Solution for r^2-4r=16 equation:


Simplifying
r2 + -4r = 16

Reorder the terms:
-4r + r2 = 16

Solving
-4r + r2 = 16

Solving for variable 'r'.

Reorder the terms:
-16 + -4r + r2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -4r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + -4r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -4r + r2 = 0 + 16
-4r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
-4r + r2 = 16

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 16 + 4

Reorder the terms:
4 + -4r + r2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + -4r + r2 = 20

Factor a perfect square on the left side:
(r + -2)(r + -2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(r + -2) equal to 4.472135955 and -4.472135955.

Subproblem 1

r + -2 = 4.472135955 Simplifying r + -2 = 4.472135955 Reorder the terms: -2 + r = 4.472135955 Solving -2 + r = 4.472135955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + r = 4.472135955 + 2 r = 4.472135955 + 2 Combine like terms: 4.472135955 + 2 = 6.472135955 r = 6.472135955 Simplifying r = 6.472135955

Subproblem 2

r + -2 = -4.472135955 Simplifying r + -2 = -4.472135955 Reorder the terms: -2 + r = -4.472135955 Solving -2 + r = -4.472135955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + r = -4.472135955 + 2 r = -4.472135955 + 2 Combine like terms: -4.472135955 + 2 = -2.472135955 r = -2.472135955 Simplifying r = -2.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. r = {6.472135955, -2.472135955}

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