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Simplifying 11r2 + -110r + -4400 = 0 Reorder the terms: -4400 + -110r + 11r2 = 0 Solving -4400 + -110r + 11r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '11'. 11(-400 + -10r + r2) = 0 Ignore the factor 11.Subproblem 1
Set the factor '(-400 + -10r + r2)' equal to zero and attempt to solve: Simplifying -400 + -10r + r2 = 0 Solving -400 + -10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -10r + 400 + r2 = 0 + 400 Reorder the terms: -400 + 400 + -10r + r2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -10r + r2 = 0 + 400 -10r + r2 = 0 + 400 Combine like terms: 0 + 400 = 400 -10r + r2 = 400 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = 400 + 25 Reorder the terms: 25 + -10r + r2 = 400 + 25 Combine like terms: 400 + 25 = 425 25 + -10r + r2 = 425 Factor a perfect square on the left side: (r + -5)(r + -5) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (r + -5) equal to 20.615528128 and -20.615528128.Subproblem 1
r + -5 = 20.615528128 Simplifying r + -5 = 20.615528128 Reorder the terms: -5 + r = 20.615528128 Solving -5 + r = 20.615528128 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + r = 20.615528128 + 5 r = 20.615528128 + 5 Combine like terms: 20.615528128 + 5 = 25.615528128 r = 25.615528128 Simplifying r = 25.615528128Subproblem 2
r + -5 = -20.615528128 Simplifying r + -5 = -20.615528128 Reorder the terms: -5 + r = -20.615528128 Solving -5 + r = -20.615528128 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + r = -20.615528128 + 5 r = -20.615528128 + 5 Combine like terms: -20.615528128 + 5 = -15.615528128 r = -15.615528128 Simplifying r = -15.615528128Solution
The solution to the problem is based on the solutions from the subproblems. r = {25.615528128, -15.615528128}Solution
r = {25.615528128, -15.615528128}
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