r^2+r-300=0

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Solution for r^2+r-300=0 equation: 


Simplifying
r2 + r + -300 = 0

Reorder the terms:
-300 + r + r2 = 0

Solving
-300 + r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + r + 300 + r2 = 0 + 300

Reorder the terms:
-300 + 300 + r + r2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + r + r2 = 0 + 300
r + r2 = 0 + 300

Combine like terms: 0 + 300 = 300
r + r2 = 300

The r term is r.  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.
r + 0.25 + r2 = 300 + 0.25

Reorder the terms:
0.25 + r + r2 = 300 + 0.25

Combine like terms: 300 + 0.25 = 300.25
0.25 + r + r2 = 300.25

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 300.25

Calculate the square root of the right side: 17.327723451

Break this problem into two subproblems by setting 
(r + 0.5) equal to 17.327723451 and -17.327723451.


Subproblem 1
r + 0.5 = 17.327723451

Simplifying
r + 0.5 = 17.327723451

Reorder the terms:
0.5 + r = 17.327723451

Solving
0.5 + r = 17.327723451

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 = 17.327723451 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 17.327723451 + -0.5
r = 17.327723451 + -0.5

Combine like terms: 17.327723451 + -0.5 = 16.827723451
r = 16.827723451

Simplifying
r = 16.827723451


Subproblem 2
r + 0.5 = -17.327723451

Simplifying
r + 0.5 = -17.327723451

Reorder the terms:
0.5 + r = -17.327723451

Solving
0.5 + r = -17.327723451

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 = -17.327723451 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -17.327723451 + -0.5
r = -17.327723451 + -0.5

Combine like terms: -17.327723451 + -0.5 = -17.827723451
r = -17.827723451

Simplifying
r = -17.827723451


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {16.827723451, -17.827723451}

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