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Simplifying 25r2 + -100r = -65 Reorder the terms: -100r + 25r2 = -65 Solving -100r + 25r2 = -65 Solving for variable 'r'. Reorder the terms: 65 + -100r + 25r2 = -65 + 65 Combine like terms: -65 + 65 = 0 65 + -100r + 25r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(13 + -20r + 5r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(13 + -20r + 5r2)' equal to zero and attempt to solve: Simplifying 13 + -20r + 5r2 = 0 Solving 13 + -20r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.6 + -4r + r2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -4r + -2.6 + r2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -4r + r2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -4r + r2 = 0 + -2.6 -4r + r2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -4r + r2 = -2.6 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 = -2.6 + 4 Reorder the terms: 4 + -4r + r2 = -2.6 + 4 Combine like terms: -2.6 + 4 = 1.4 4 + -4r + r2 = 1.4 Factor a perfect square on the left side: (r + -2)(r + -2) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (r + -2) equal to 1.183215957 and -1.183215957.Subproblem 1
r + -2 = 1.183215957 Simplifying r + -2 = 1.183215957 Reorder the terms: -2 + r = 1.183215957 Solving -2 + r = 1.183215957 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 = 1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + r = 1.183215957 + 2 r = 1.183215957 + 2 Combine like terms: 1.183215957 + 2 = 3.183215957 r = 3.183215957 Simplifying r = 3.183215957Subproblem 2
r + -2 = -1.183215957 Simplifying r + -2 = -1.183215957 Reorder the terms: -2 + r = -1.183215957 Solving -2 + r = -1.183215957 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 = -1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + r = -1.183215957 + 2 r = -1.183215957 + 2 Combine like terms: -1.183215957 + 2 = 0.816784043 r = 0.816784043 Simplifying r = 0.816784043Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.183215957, 0.816784043}Solution
r = {3.183215957, 0.816784043}
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