30=r*r+2r

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Solution for 30=r*r+2r equation:


Simplifying
30 = r * r + 2r

Multiply r * r
30 = r2 + 2r

Reorder the terms:
30 = 2r + r2

Solving
30 = 2r + r2

Solving for variable 'r'.

Reorder the terms:
30 + -2r + -1r2 = 2r + -2r + r2 + -1r2

Combine like terms: 2r + -2r = 0
30 + -2r + -1r2 = 0 + r2 + -1r2
30 + -2r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
30 + -2r + -1r2 = 0

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

Divide each side by '-1'.
-30 + 2r + r2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2r + 30 + r2 = 0 + 30

Reorder the terms:
-30 + 30 + 2r + r2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2r + r2 = 0 + 30
2r + r2 = 0 + 30

Combine like terms: 0 + 30 = 30
2r + r2 = 30

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 = 30 + 1

Reorder the terms:
1 + 2r + r2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2r + r2 = 31

Factor a perfect square on the left side:
(r + 1)(r + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(r + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1

r + 1 = 5.567764363 Simplifying r + 1 = 5.567764363 Reorder the terms: 1 + r = 5.567764363 Solving 1 + r = 5.567764363 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 = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + r = 5.567764363 + -1 r = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 r = 4.567764363 Simplifying r = 4.567764363

Subproblem 2

r + 1 = -5.567764363 Simplifying r + 1 = -5.567764363 Reorder the terms: 1 + r = -5.567764363 Solving 1 + r = -5.567764363 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 = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + r = -5.567764363 + -1 r = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 r = -6.567764363 Simplifying r = -6.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.567764363, -6.567764363}

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