r^2-20r=-65

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Solution for r^2-20r=-65 equation:


Simplifying
r2 + -20r = -65

Reorder the terms:
-20r + r2 = -65

Solving
-20r + r2 = -65

Solving for variable 'r'.

Reorder the terms:
65 + -20r + r2 = -65 + 65

Combine like terms: -65 + 65 = 0
65 + -20r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-65' to each side of the equation.
65 + -20r + -65 + r2 = 0 + -65

Reorder the terms:
65 + -65 + -20r + r2 = 0 + -65

Combine like terms: 65 + -65 = 0
0 + -20r + r2 = 0 + -65
-20r + r2 = 0 + -65

Combine like terms: 0 + -65 = -65
-20r + r2 = -65

The r term is -20r.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20r + 100 + r2 = -65 + 100

Reorder the terms:
100 + -20r + r2 = -65 + 100

Combine like terms: -65 + 100 = 35
100 + -20r + r2 = 35

Factor a perfect square on the left side:
(r + -10)(r + -10) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(r + -10) equal to 5.916079783 and -5.916079783.

Subproblem 1

r + -10 = 5.916079783 Simplifying r + -10 = 5.916079783 Reorder the terms: -10 + r = 5.916079783 Solving -10 + r = 5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 5.916079783 + 10 Combine like terms: -10 + 10 = 0 0 + r = 5.916079783 + 10 r = 5.916079783 + 10 Combine like terms: 5.916079783 + 10 = 15.916079783 r = 15.916079783 Simplifying r = 15.916079783

Subproblem 2

r + -10 = -5.916079783 Simplifying r + -10 = -5.916079783 Reorder the terms: -10 + r = -5.916079783 Solving -10 + r = -5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -5.916079783 + 10 Combine like terms: -10 + 10 = 0 0 + r = -5.916079783 + 10 r = -5.916079783 + 10 Combine like terms: -5.916079783 + 10 = 4.083920217 r = 4.083920217 Simplifying r = 4.083920217

Solution

The solution to the problem is based on the solutions from the subproblems. r = {15.916079783, 4.083920217}

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