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Simplifying r2 + -35r + 70 = 0 Reorder the terms: 70 + -35r + r2 = 0 Solving 70 + -35r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -35r + -70 + r2 = 0 + -70 Reorder the terms: 70 + -70 + -35r + r2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -35r + r2 = 0 + -70 -35r + r2 = 0 + -70 Combine like terms: 0 + -70 = -70 -35r + r2 = -70 The r term is -35r. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35r + 306.25 + r2 = -70 + 306.25 Reorder the terms: 306.25 + -35r + r2 = -70 + 306.25 Combine like terms: -70 + 306.25 = 236.25 306.25 + -35r + r2 = 236.25 Factor a perfect square on the left side: (r + -17.5)(r + -17.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (r + -17.5) equal to 15.370426149 and -15.370426149.Subproblem 1
r + -17.5 = 15.370426149 Simplifying r + -17.5 = 15.370426149 Reorder the terms: -17.5 + r = 15.370426149 Solving -17.5 + r = 15.370426149 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + r = 15.370426149 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + r = 15.370426149 + 17.5 r = 15.370426149 + 17.5 Combine like terms: 15.370426149 + 17.5 = 32.870426149 r = 32.870426149 Simplifying r = 32.870426149Subproblem 2
r + -17.5 = -15.370426149 Simplifying r + -17.5 = -15.370426149 Reorder the terms: -17.5 + r = -15.370426149 Solving -17.5 + r = -15.370426149 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + r = -15.370426149 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + r = -15.370426149 + 17.5 r = -15.370426149 + 17.5 Combine like terms: -15.370426149 + 17.5 = 2.129573851 r = 2.129573851 Simplifying r = 2.129573851Solution
The solution to the problem is based on the solutions from the subproblems. r = {32.870426149, 2.129573851}
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