r^2+8r-30=0

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Solution for r^2+8r-30=0 equation: 


Simplifying
r2 + 8r + -30 = 0

Reorder the terms:
-30 + 8r + r2 = 0

Solving
-30 + 8r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 8r + 30 + r2 = 0 + 30

Reorder the terms:
-30 + 30 + 8r + r2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 8r + r2 = 0 + 30
8r + r2 = 0 + 30

Combine like terms: 0 + 30 = 30
8r + r2 = 30

The r term is 8r.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r + 16 + r2 = 30 + 16

Reorder the terms:
16 + 8r + r2 = 30 + 16

Combine like terms: 30 + 16 = 46
16 + 8r + r2 = 46

Factor a perfect square on the left side:
(r + 4)(r + 4) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(r + 4) equal to 6.782329983 and -6.782329983.


Subproblem 1
r + 4 = 6.782329983

Simplifying
r + 4 = 6.782329983

Reorder the terms:
4 + r = 6.782329983

Solving
4 + r = 6.782329983

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + r = 6.782329983 + -4

Combine like terms: 4 + -4 = 0
0 + r = 6.782329983 + -4
r = 6.782329983 + -4

Combine like terms: 6.782329983 + -4 = 2.782329983
r = 2.782329983

Simplifying
r = 2.782329983


Subproblem 2
r + 4 = -6.782329983

Simplifying
r + 4 = -6.782329983

Reorder the terms:
4 + r = -6.782329983

Solving
4 + r = -6.782329983

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + r = -6.782329983 + -4

Combine like terms: 4 + -4 = 0
0 + r = -6.782329983 + -4
r = -6.782329983 + -4

Combine like terms: -6.782329983 + -4 = -10.782329983
r = -10.782329983

Simplifying
r = -10.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.782329983, -10.782329983}

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