R^2-320R+7600=0

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Solution for R^2-320R+7600=0 equation:


Simplifying
R2 + -320R + 7600 = 0

Reorder the terms:
7600 + -320R + R2 = 0

Solving
7600 + -320R + R2 = 0

Solving for variable 'R'.

Begin completing the square.

Move the constant term to the right:

Add '-7600' to each side of the equation.
7600 + -320R + -7600 + R2 = 0 + -7600

Reorder the terms:
7600 + -7600 + -320R + R2 = 0 + -7600

Combine like terms: 7600 + -7600 = 0
0 + -320R + R2 = 0 + -7600
-320R + R2 = 0 + -7600

Combine like terms: 0 + -7600 = -7600
-320R + R2 = -7600

The R term is -320R.  Take half its coefficient (-160).
Square it (25600) and add it to both sides.

Add '25600' to each side of the equation.
-320R + 25600 + R2 = -7600 + 25600

Reorder the terms:
25600 + -320R + R2 = -7600 + 25600

Combine like terms: -7600 + 25600 = 18000
25600 + -320R + R2 = 18000

Factor a perfect square on the left side:
(R + -160)(R + -160) = 18000

Calculate the square root of the right side: 134.16407865

Break this problem into two subproblems by setting 
(R + -160) equal to 134.16407865 and -134.16407865.


Subproblem 1
R + -160 = 134.16407865

Simplifying
R + -160 = 134.16407865

Reorder the terms:
-160 + R = 134.16407865

Solving
-160 + R = 134.16407865

Solving for variable 'R'.

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

Add '160' to each side of the equation.
-160 + 160 + R = 134.16407865 + 160

Combine like terms: -160 + 160 = 0
0 + R = 134.16407865 + 160
R = 134.16407865 + 160

Combine like terms: 134.16407865 + 160 = 294.16407865
R = 294.16407865

Simplifying
R = 294.16407865


Subproblem 2
R + -160 = -134.16407865

Simplifying
R + -160 = -134.16407865

Reorder the terms:
-160 + R = -134.16407865

Solving
-160 + R = -134.16407865

Solving for variable 'R'.

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

Add '160' to each side of the equation.
-160 + 160 + R = -134.16407865 + 160

Combine like terms: -160 + 160 = 0
0 + R = -134.16407865 + 160
R = -134.16407865 + 160

Combine like terms: -134.16407865 + 160 = 25.83592135
R = 25.83592135

Simplifying
R = 25.83592135


Solution
The solution to the problem is based on the solutions
from the subproblems.
R = {294.16407865, 25.83592135}

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