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Simplifying 5r2 + -8r = 3 Reorder the terms: -8r + 5r2 = 3 Solving -8r + 5r2 = 3 Solving for variable 'r'. Reorder the terms: -3 + -8r + 5r2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -8r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.6r + r2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.6r + 0.6 + r2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.6r + r2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.6r + r2 = 0 + 0.6 -1.6r + r2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.6r + r2 = 0.6 The r term is -1.6r. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6r + 0.64 + r2 = 0.6 + 0.64 Reorder the terms: 0.64 + -1.6r + r2 = 0.6 + 0.64 Combine like terms: 0.6 + 0.64 = 1.24 0.64 + -1.6r + r2 = 1.24 Factor a perfect square on the left side: (r + -0.8)(r + -0.8) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (r + -0.8) equal to 1.113552873 and -1.113552873.Subproblem 1
r + -0.8 = 1.113552873 Simplifying r + -0.8 = 1.113552873 Reorder the terms: -0.8 + r = 1.113552873 Solving -0.8 + r = 1.113552873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + r = 1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + r = 1.113552873 + 0.8 r = 1.113552873 + 0.8 Combine like terms: 1.113552873 + 0.8 = 1.913552873 r = 1.913552873 Simplifying r = 1.913552873Subproblem 2
r + -0.8 = -1.113552873 Simplifying r + -0.8 = -1.113552873 Reorder the terms: -0.8 + r = -1.113552873 Solving -0.8 + r = -1.113552873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + r = -1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + r = -1.113552873 + 0.8 r = -1.113552873 + 0.8 Combine like terms: -1.113552873 + 0.8 = -0.313552873 r = -0.313552873 Simplifying r = -0.313552873Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.913552873, -0.313552873}
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