20r^2-80r+64=

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Solution for 20r^2-80r+64= equation:


Simplifying
20r2 + -80r + 64 = 0

Reorder the terms:
64 + -80r + 20r2 = 0

Solving
64 + -80r + 20r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -20r + 5r2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(16 + -20r + 5r2)' equal to zero and attempt to solve: Simplifying 16 + -20r + 5r2 = 0 Solving 16 + -20r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -4r + r2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -4r + -3.2 + r2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -4r + r2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -4r + r2 = 0 + -3.2 -4r + r2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -4r + r2 = -3.2 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = -3.2 + 4 Reorder the terms: 4 + -4r + r2 = -3.2 + 4 Combine like terms: -3.2 + 4 = 0.8 4 + -4r + r2 = 0.8 Factor a perfect square on the left side: (r + -2)(r + -2) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (r + -2) equal to 0.894427191 and -0.894427191.

Subproblem 1

r + -2 = 0.894427191 Simplifying r + -2 = 0.894427191 Reorder the terms: -2 + r = 0.894427191 Solving -2 + r = 0.894427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 0.894427191 + 2 Combine like terms: -2 + 2 = 0 0 + r = 0.894427191 + 2 r = 0.894427191 + 2 Combine like terms: 0.894427191 + 2 = 2.894427191 r = 2.894427191 Simplifying r = 2.894427191

Subproblem 2

r + -2 = -0.894427191 Simplifying r + -2 = -0.894427191 Reorder the terms: -2 + r = -0.894427191 Solving -2 + r = -0.894427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -0.894427191 + 2 Combine like terms: -2 + 2 = 0 0 + r = -0.894427191 + 2 r = -0.894427191 + 2 Combine like terms: -0.894427191 + 2 = 1.105572809 r = 1.105572809 Simplifying r = 1.105572809

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.894427191, 1.105572809}

Solution

r = {2.894427191, 1.105572809}

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