r^2-20r+91=8

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Solution for r^2-20r+91=8 equation:


Simplifying
r2 + -20r + 91 = 8

Reorder the terms:
91 + -20r + r2 = 8

Solving
91 + -20r + r2 = 8

Solving for variable 'r'.

Reorder the terms:
91 + -8 + -20r + r2 = 8 + -8

Combine like terms: 91 + -8 = 83
83 + -20r + r2 = 8 + -8

Combine like terms: 8 + -8 = 0
83 + -20r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-83' to each side of the equation.
83 + -20r + -83 + r2 = 0 + -83

Reorder the terms:
83 + -83 + -20r + r2 = 0 + -83

Combine like terms: 83 + -83 = 0
0 + -20r + r2 = 0 + -83
-20r + r2 = 0 + -83

Combine like terms: 0 + -83 = -83
-20r + r2 = -83

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 = -83 + 100

Reorder the terms:
100 + -20r + r2 = -83 + 100

Combine like terms: -83 + 100 = 17
100 + -20r + r2 = 17

Factor a perfect square on the left side:
(r + -10)(r + -10) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(r + -10) equal to 4.123105626 and -4.123105626.

Subproblem 1

r + -10 = 4.123105626 Simplifying r + -10 = 4.123105626 Reorder the terms: -10 + r = 4.123105626 Solving -10 + r = 4.123105626 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 = 4.123105626 + 10 Combine like terms: -10 + 10 = 0 0 + r = 4.123105626 + 10 r = 4.123105626 + 10 Combine like terms: 4.123105626 + 10 = 14.123105626 r = 14.123105626 Simplifying r = 14.123105626

Subproblem 2

r + -10 = -4.123105626 Simplifying r + -10 = -4.123105626 Reorder the terms: -10 + r = -4.123105626 Solving -10 + r = -4.123105626 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 = -4.123105626 + 10 Combine like terms: -10 + 10 = 0 0 + r = -4.123105626 + 10 r = -4.123105626 + 10 Combine like terms: -4.123105626 + 10 = 5.876894374 r = 5.876894374 Simplifying r = 5.876894374

Solution

The solution to the problem is based on the solutions from the subproblems. r = {14.123105626, 5.876894374}

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