R^2+20R-1=-8

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Solution for R^2+20R-1=-8 equation: 


Simplifying
R2 + 20R + -1 = -8

Reorder the terms:
-1 + 20R + R2 = -8

Solving
-1 + 20R + R2 = -8

Solving for variable 'R'.

Reorder the terms:
-1 + 8 + 20R + R2 = -8 + 8

Combine like terms: -1 + 8 = 7
7 + 20R + R2 = -8 + 8

Combine like terms: -8 + 8 = 0
7 + 20R + R2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 20R + -7 + R2 = 0 + -7

Reorder the terms:
7 + -7 + 20R + R2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 20R + R2 = 0 + -7
20R + R2 = 0 + -7

Combine like terms: 0 + -7 = -7
20R + R2 = -7

The R term is 20R.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20R + 100 + R2 = -7 + 100

Reorder the terms:
100 + 20R + R2 = -7 + 100

Combine like terms: -7 + 100 = 93
100 + 20R + R2 = 93

Factor a perfect square on the left side:
(R + 10)(R + 10) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(R + 10) equal to 9.643650761 and -9.643650761.


Subproblem 1
R + 10 = 9.643650761

Simplifying
R + 10 = 9.643650761

Reorder the terms:
10 + R = 9.643650761

Solving
10 + R = 9.643650761

Solving for variable 'R'.

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

Add '-10' to each side of the equation.
10 + -10 + R = 9.643650761 + -10

Combine like terms: 10 + -10 = 0
0 + R = 9.643650761 + -10
R = 9.643650761 + -10

Combine like terms: 9.643650761 + -10 = -0.356349239
R = -0.356349239

Simplifying
R = -0.356349239


Subproblem 2
R + 10 = -9.643650761

Simplifying
R + 10 = -9.643650761

Reorder the terms:
10 + R = -9.643650761

Solving
10 + R = -9.643650761

Solving for variable 'R'.

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

Add '-10' to each side of the equation.
10 + -10 + R = -9.643650761 + -10

Combine like terms: 10 + -10 = 0
0 + R = -9.643650761 + -10
R = -9.643650761 + -10

Combine like terms: -9.643650761 + -10 = -19.643650761
R = -19.643650761

Simplifying
R = -19.643650761


Solution
The solution to the problem is based on the solutions
from the subproblems.
R = {-0.356349239, -19.643650761}

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