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Simplifying -7r2 + 140r + 100 = 0 Reorder the terms: 100 + 140r + -7r2 = 0 Solving 100 + 140r + -7r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -14.28571429 + -20r + r2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + -20r + 14.28571429 + r2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + -20r + r2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + -20r + r2 = 0 + 14.28571429 -20r + r2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 -20r + r2 = 14.28571429 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 = 14.28571429 + 100 Reorder the terms: 100 + -20r + r2 = 14.28571429 + 100 Combine like terms: 14.28571429 + 100 = 114.28571429 100 + -20r + r2 = 114.28571429 Factor a perfect square on the left side: (r + -10)(r + -10) = 114.28571429 Calculate the square root of the right side: 10.690449677 Break this problem into two subproblems by setting (r + -10) equal to 10.690449677 and -10.690449677.Subproblem 1
r + -10 = 10.690449677 Simplifying r + -10 = 10.690449677 Reorder the terms: -10 + r = 10.690449677 Solving -10 + r = 10.690449677 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 = 10.690449677 + 10 Combine like terms: -10 + 10 = 0 0 + r = 10.690449677 + 10 r = 10.690449677 + 10 Combine like terms: 10.690449677 + 10 = 20.690449677 r = 20.690449677 Simplifying r = 20.690449677Subproblem 2
r + -10 = -10.690449677 Simplifying r + -10 = -10.690449677 Reorder the terms: -10 + r = -10.690449677 Solving -10 + r = -10.690449677 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 = -10.690449677 + 10 Combine like terms: -10 + 10 = 0 0 + r = -10.690449677 + 10 r = -10.690449677 + 10 Combine like terms: -10.690449677 + 10 = -0.690449677 r = -0.690449677 Simplifying r = -0.690449677Solution
The solution to the problem is based on the solutions from the subproblems. r = {20.690449677, -0.690449677}
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