r^2-24r+64=0

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Solution for r^2-24r+64=0 equation:


Simplifying
r2 + -24r + 64 = 0

Reorder the terms:
64 + -24r + r2 = 0

Solving
64 + -24r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -24r + -64 + r2 = 0 + -64

Reorder the terms:
64 + -64 + -24r + r2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -24r + r2 = 0 + -64
-24r + r2 = 0 + -64

Combine like terms: 0 + -64 = -64
-24r + r2 = -64

The r term is -24r.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24r + 144 + r2 = -64 + 144

Reorder the terms:
144 + -24r + r2 = -64 + 144

Combine like terms: -64 + 144 = 80
144 + -24r + r2 = 80

Factor a perfect square on the left side:
(r + -12)(r + -12) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(r + -12) equal to 8.94427191 and -8.94427191.

Subproblem 1

r + -12 = 8.94427191 Simplifying r + -12 = 8.94427191 Reorder the terms: -12 + r = 8.94427191 Solving -12 + r = 8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + r = 8.94427191 + 12 Combine like terms: -12 + 12 = 0 0 + r = 8.94427191 + 12 r = 8.94427191 + 12 Combine like terms: 8.94427191 + 12 = 20.94427191 r = 20.94427191 Simplifying r = 20.94427191

Subproblem 2

r + -12 = -8.94427191 Simplifying r + -12 = -8.94427191 Reorder the terms: -12 + r = -8.94427191 Solving -12 + r = -8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + r = -8.94427191 + 12 Combine like terms: -12 + 12 = 0 0 + r = -8.94427191 + 12 r = -8.94427191 + 12 Combine like terms: -8.94427191 + 12 = 3.05572809 r = 3.05572809 Simplifying r = 3.05572809

Solution

The solution to the problem is based on the solutions from the subproblems. r = {20.94427191, 3.05572809}

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