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Simplifying 8r2 + 10r = 17 Reorder the terms: 10r + 8r2 = 17 Solving 10r + 8r2 = 17 Solving for variable 'r'. Reorder the terms: -17 + 10r + 8r2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 10r + 8r2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + 1.25r + r2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 1.25r + 2.125 + r2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 1.25r + r2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 1.25r + r2 = 0 + 2.125 1.25r + r2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 1.25r + r2 = 2.125 The r term is 1.25r. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25r + 0.390625 + r2 = 2.125 + 0.390625 Reorder the terms: 0.390625 + 1.25r + r2 = 2.125 + 0.390625 Combine like terms: 2.125 + 0.390625 = 2.515625 0.390625 + 1.25r + r2 = 2.515625 Factor a perfect square on the left side: (r + 0.625)(r + 0.625) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (r + 0.625) equal to 1.586072193 and -1.586072193.Subproblem 1
r + 0.625 = 1.586072193 Simplifying r + 0.625 = 1.586072193 Reorder the terms: 0.625 + r = 1.586072193 Solving 0.625 + r = 1.586072193 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + r = 1.586072193 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + r = 1.586072193 + -0.625 r = 1.586072193 + -0.625 Combine like terms: 1.586072193 + -0.625 = 0.961072193 r = 0.961072193 Simplifying r = 0.961072193Subproblem 2
r + 0.625 = -1.586072193 Simplifying r + 0.625 = -1.586072193 Reorder the terms: 0.625 + r = -1.586072193 Solving 0.625 + r = -1.586072193 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + r = -1.586072193 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + r = -1.586072193 + -0.625 r = -1.586072193 + -0.625 Combine like terms: -1.586072193 + -0.625 = -2.211072193 r = -2.211072193 Simplifying r = -2.211072193Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.961072193, -2.211072193}
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