R^2+50R-375=0

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Solution for R^2+50R-375=0 equation: 


Simplifying
R2 + 50R + -375 = 0

Reorder the terms:
-375 + 50R + R2 = 0

Solving
-375 + 50R + R2 = 0

Solving for variable 'R'.

Begin completing the square.

Move the constant term to the right:

Add '375' to each side of the equation.
-375 + 50R + 375 + R2 = 0 + 375

Reorder the terms:
-375 + 375 + 50R + R2 = 0 + 375

Combine like terms: -375 + 375 = 0
0 + 50R + R2 = 0 + 375
50R + R2 = 0 + 375

Combine like terms: 0 + 375 = 375
50R + R2 = 375

The R term is 50R.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50R + 625 + R2 = 375 + 625

Reorder the terms:
625 + 50R + R2 = 375 + 625

Combine like terms: 375 + 625 = 1000
625 + 50R + R2 = 1000

Factor a perfect square on the left side:
(R + 25)(R + 25) = 1000

Calculate the square root of the right side: 31.622776602

Break this problem into two subproblems by setting 
(R + 25) equal to 31.622776602 and -31.622776602.


Subproblem 1
R + 25 = 31.622776602

Simplifying
R + 25 = 31.622776602

Reorder the terms:
25 + R = 31.622776602

Solving
25 + R = 31.622776602

Solving for variable 'R'.

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

Add '-25' to each side of the equation.
25 + -25 + R = 31.622776602 + -25

Combine like terms: 25 + -25 = 0
0 + R = 31.622776602 + -25
R = 31.622776602 + -25

Combine like terms: 31.622776602 + -25 = 6.622776602
R = 6.622776602

Simplifying
R = 6.622776602


Subproblem 2
R + 25 = -31.622776602

Simplifying
R + 25 = -31.622776602

Reorder the terms:
25 + R = -31.622776602

Solving
25 + R = -31.622776602

Solving for variable 'R'.

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

Add '-25' to each side of the equation.
25 + -25 + R = -31.622776602 + -25

Combine like terms: 25 + -25 = 0
0 + R = -31.622776602 + -25
R = -31.622776602 + -25

Combine like terms: -31.622776602 + -25 = -56.622776602
R = -56.622776602

Simplifying
R = -56.622776602


Solution
The solution to the problem is based on the solutions
from the subproblems.
R = {6.622776602, -56.622776602}

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