8=r(r+4)

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Solution for 8=r(r+4) equation:


Simplifying
8 = r(r + 4)

Reorder the terms:
8 = r(4 + r)
8 = (4 * r + r * r)
8 = (4r + r2)

Solving
8 = 4r + r2

Solving for variable 'r'.

Reorder the terms:
8 + -4r + -1r2 = 4r + -4r + r2 + -1r2

Combine like terms: 4r + -4r = 0
8 + -4r + -1r2 = 0 + r2 + -1r2
8 + -4r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
8 + -4r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8 + 4r + r2 = 0

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 = 1.464101615 r = 1.464101615 Simplifying r = 1.464101615

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 = -5.464101615 r = -5.464101615 Simplifying r = -5.464101615

Solution

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

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