5r^2-55r-150=0

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Solution for 5r^2-55r-150=0 equation: 


Simplifying
5r2 + -55r + -150 = 0

Reorder the terms:
-150 + -55r + 5r2 = 0

Solving
-150 + -55r + 5r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-30 + -11r + r2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-30 + -11r + r2)' equal to zero and attempt to solve:

Simplifying
-30 + -11r + r2 = 0

Solving
-30 + -11r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -11r + 30 + r2 = 0 + 30

Reorder the terms:
-30 + 30 + -11r + r2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -11r + r2 = 0 + 30
-11r + r2 = 0 + 30

Combine like terms: 0 + 30 = 30
-11r + r2 = 30

The r term is -11r.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11r + 30.25 + r2 = 30 + 30.25

Reorder the terms:
30.25 + -11r + r2 = 30 + 30.25

Combine like terms: 30 + 30.25 = 60.25
30.25 + -11r + r2 = 60.25

Factor a perfect square on the left side:
(r + -5.5)(r + -5.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(r + -5.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
r + -5.5 = 7.762087348

Simplifying
r + -5.5 = 7.762087348

Reorder the terms:
-5.5 + r = 7.762087348

Solving
-5.5 + r = 7.762087348

Solving for variable 'r'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + r = 7.762087348 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + r = 7.762087348 + 5.5
r = 7.762087348 + 5.5

Combine like terms: 7.762087348 + 5.5 = 13.262087348
r = 13.262087348

Simplifying
r = 13.262087348


Subproblem 2
r + -5.5 = -7.762087348

Simplifying
r + -5.5 = -7.762087348

Reorder the terms:
-5.5 + r = -7.762087348

Solving
-5.5 + r = -7.762087348

Solving for variable 'r'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + r = -7.762087348 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + r = -7.762087348 + 5.5
r = -7.762087348 + 5.5

Combine like terms: -7.762087348 + 5.5 = -2.262087348
r = -2.262087348

Simplifying
r = -2.262087348


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {13.262087348, -2.262087348}
Solution
r = {13.262087348, -2.262087348}

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