r^2-30r=41

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Solution for r^2-30r=41 equation:


Simplifying
r2 + -30r = 41

Reorder the terms:
-30r + r2 = 41

Solving
-30r + r2 = 41

Solving for variable 'r'.

Reorder the terms:
-41 + -30r + r2 = 41 + -41

Combine like terms: 41 + -41 = 0
-41 + -30r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -30r + 41 + r2 = 0 + 41

Reorder the terms:
-41 + 41 + -30r + r2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -30r + r2 = 0 + 41
-30r + r2 = 0 + 41

Combine like terms: 0 + 41 = 41
-30r + r2 = 41

The r term is -30r.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30r + 225 + r2 = 41 + 225

Reorder the terms:
225 + -30r + r2 = 41 + 225

Combine like terms: 41 + 225 = 266
225 + -30r + r2 = 266

Factor a perfect square on the left side:
(r + -15)(r + -15) = 266

Calculate the square root of the right side: 16.30950643

Break this problem into two subproblems by setting 
(r + -15) equal to 16.30950643 and -16.30950643.

Subproblem 1

r + -15 = 16.30950643 Simplifying r + -15 = 16.30950643 Reorder the terms: -15 + r = 16.30950643 Solving -15 + r = 16.30950643 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = 16.30950643 + 15 Combine like terms: -15 + 15 = 0 0 + r = 16.30950643 + 15 r = 16.30950643 + 15 Combine like terms: 16.30950643 + 15 = 31.30950643 r = 31.30950643 Simplifying r = 31.30950643

Subproblem 2

r + -15 = -16.30950643 Simplifying r + -15 = -16.30950643 Reorder the terms: -15 + r = -16.30950643 Solving -15 + r = -16.30950643 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = -16.30950643 + 15 Combine like terms: -15 + 15 = 0 0 + r = -16.30950643 + 15 r = -16.30950643 + 15 Combine like terms: -16.30950643 + 15 = -1.30950643 r = -1.30950643 Simplifying r = -1.30950643

Solution

The solution to the problem is based on the solutions from the subproblems. r = {31.30950643, -1.30950643}

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