R^2-R-30=30

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Solution for R^2-R-30=30 equation: 


Simplifying
R2 + -1R + -30 = 30

Reorder the terms:
-30 + -1R + R2 = 30

Solving
-30 + -1R + R2 = 30

Solving for variable 'R'.

Reorder the terms:
-30 + -30 + -1R + R2 = 30 + -30

Combine like terms: -30 + -30 = -60
-60 + -1R + R2 = 30 + -30

Combine like terms: 30 + -30 = 0
-60 + -1R + R2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -1R + 60 + R2 = 0 + 60

Reorder the terms:
-60 + 60 + -1R + R2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -1R + R2 = 0 + 60
-1R + R2 = 0 + 60

Combine like terms: 0 + 60 = 60
-1R + R2 = 60

The R term is -1R.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1R + 0.25 + R2 = 60 + 0.25

Reorder the terms:
0.25 + -1R + R2 = 60 + 0.25

Combine like terms: 60 + 0.25 = 60.25
0.25 + -1R + R2 = 60.25

Factor a perfect square on the left side:
(R + -0.5)(R + -0.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(R + -0.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
R + -0.5 = 7.762087348

Simplifying
R + -0.5 = 7.762087348

Reorder the terms:
-0.5 + R = 7.762087348

Solving
-0.5 + R = 7.762087348

Solving for variable 'R'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + R = 7.762087348 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + R = 7.762087348 + 0.5
R = 7.762087348 + 0.5

Combine like terms: 7.762087348 + 0.5 = 8.262087348
R = 8.262087348

Simplifying
R = 8.262087348


Subproblem 2
R + -0.5 = -7.762087348

Simplifying
R + -0.5 = -7.762087348

Reorder the terms:
-0.5 + R = -7.762087348

Solving
-0.5 + R = -7.762087348

Solving for variable 'R'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + R = -7.762087348 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + R = -7.762087348 + 0.5
R = -7.762087348 + 0.5

Combine like terms: -7.762087348 + 0.5 = -7.262087348
R = -7.262087348

Simplifying
R = -7.262087348


Solution
The solution to the problem is based on the solutions
from the subproblems.
R = {8.262087348, -7.262087348}

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