r^2-4r+16=8+16

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Solution for r^2-4r+16=8+16 equation:


Simplifying
r2 + -4r + 16 = 8 + 16

Reorder the terms:
16 + -4r + r2 = 8 + 16

Combine like terms: 8 + 16 = 24
16 + -4r + r2 = 24

Solving
16 + -4r + r2 = 24

Solving for variable 'r'.

Reorder the terms:
16 + -24 + -4r + r2 = 24 + -24

Combine like terms: 16 + -24 = -8
-8 + -4r + r2 = 24 + -24

Combine like terms: 24 + -24 = 0
-8 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4r + 8 + r2 = 0 + 8

Reorder the terms:
-8 + 8 + -4r + r2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4r + r2 = 0 + 8
-4r + r2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4r + r2 = 8

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 = 8 + 4

Reorder the terms:
4 + -4r + r2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + -4r + r2 = 12

Factor a perfect square on the left side:
(r + -2)(r + -2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(r + -2) equal to 3.464101615 and -3.464101615.

Subproblem 1

r + -2 = 3.464101615 Simplifying r + -2 = 3.464101615 Reorder the terms: -2 + r = 3.464101615 Solving -2 + r = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + r = 3.464101615 + 2 r = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 r = 5.464101615 Simplifying r = 5.464101615

Subproblem 2

r + -2 = -3.464101615 Simplifying r + -2 = -3.464101615 Reorder the terms: -2 + r = -3.464101615 Solving -2 + r = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + r = -3.464101615 + 2 r = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 r = -1.464101615 Simplifying r = -1.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.464101615, -1.464101615}

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