r^2=35-5r

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Solution for r^2=35-5r equation:


Simplifying
r2 = 35 + -5r

Solving
r2 = 35 + -5r

Solving for variable 'r'.

Reorder the terms:
-35 + 5r + r2 = 35 + -5r + -35 + 5r

Reorder the terms:
-35 + 5r + r2 = 35 + -35 + -5r + 5r

Combine like terms: 35 + -35 = 0
-35 + 5r + r2 = 0 + -5r + 5r
-35 + 5r + r2 = -5r + 5r

Combine like terms: -5r + 5r = 0
-35 + 5r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 5r + 35 + r2 = 0 + 35

Reorder the terms:
-35 + 35 + 5r + r2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 5r + r2 = 0 + 35
5r + r2 = 0 + 35

Combine like terms: 0 + 35 = 35
5r + r2 = 35

The r term is 5r.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5r + 6.25 + r2 = 35 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 35 + 6.25

Combine like terms: 35 + 6.25 = 41.25
6.25 + 5r + r2 = 41.25

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(r + 2.5) equal to 6.422616289 and -6.422616289.

Subproblem 1

r + 2.5 = 6.422616289 Simplifying r + 2.5 = 6.422616289 Reorder the terms: 2.5 + r = 6.422616289 Solving 2.5 + r = 6.422616289 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 6.422616289 + -2.5 r = 6.422616289 + -2.5 Combine like terms: 6.422616289 + -2.5 = 3.922616289 r = 3.922616289 Simplifying r = 3.922616289

Subproblem 2

r + 2.5 = -6.422616289 Simplifying r + 2.5 = -6.422616289 Reorder the terms: 2.5 + r = -6.422616289 Solving 2.5 + r = -6.422616289 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -6.422616289 + -2.5 r = -6.422616289 + -2.5 Combine like terms: -6.422616289 + -2.5 = -8.922616289 r = -8.922616289 Simplifying r = -8.922616289

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.922616289, -8.922616289}

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