r^2+2r=45

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Solution for r^2+2r=45 equation:


Simplifying
r2 + 2r = 45

Reorder the terms:
2r + r2 = 45

Solving
2r + r2 = 45

Solving for variable 'r'.

Reorder the terms:
-45 + 2r + r2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 2r + 45 + r2 = 0 + 45

Reorder the terms:
-45 + 45 + 2r + r2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 2r + r2 = 0 + 45
2r + r2 = 0 + 45

Combine like terms: 0 + 45 = 45
2r + r2 = 45

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 45 + 1

Reorder the terms:
1 + 2r + r2 = 45 + 1

Combine like terms: 45 + 1 = 46
1 + 2r + r2 = 46

Factor a perfect square on the left side:
(r + 1)(r + 1) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(r + 1) equal to 6.782329983 and -6.782329983.

Subproblem 1

r + 1 = 6.782329983 Simplifying r + 1 = 6.782329983 Reorder the terms: 1 + r = 6.782329983 Solving 1 + r = 6.782329983 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + r = 6.782329983 + -1 r = 6.782329983 + -1 Combine like terms: 6.782329983 + -1 = 5.782329983 r = 5.782329983 Simplifying r = 5.782329983

Subproblem 2

r + 1 = -6.782329983 Simplifying r + 1 = -6.782329983 Reorder the terms: 1 + r = -6.782329983 Solving 1 + r = -6.782329983 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + r = -6.782329983 + -1 r = -6.782329983 + -1 Combine like terms: -6.782329983 + -1 = -7.782329983 r = -7.782329983 Simplifying r = -7.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.782329983, -7.782329983}

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