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Simplifying 4r2 + 5r + -5 = 0 Reorder the terms: -5 + 5r + 4r2 = 0 Solving -5 + 5r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 1.25r + r2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.25r + 1.25 + r2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.25r + r2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.25r + r2 = 0 + 1.25 1.25r + r2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.25r + r2 = 1.25 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 = 1.25 + 0.390625 Reorder the terms: 0.390625 + 1.25r + r2 = 1.25 + 0.390625 Combine like terms: 1.25 + 0.390625 = 1.640625 0.390625 + 1.25r + r2 = 1.640625 Factor a perfect square on the left side: (r + 0.625)(r + 0.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (r + 0.625) equal to 1.280868846 and -1.280868846.Subproblem 1
r + 0.625 = 1.280868846 Simplifying r + 0.625 = 1.280868846 Reorder the terms: 0.625 + r = 1.280868846 Solving 0.625 + r = 1.280868846 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 = 1.280868846 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + r = 1.280868846 + -0.625 r = 1.280868846 + -0.625 Combine like terms: 1.280868846 + -0.625 = 0.655868846 r = 0.655868846 Simplifying r = 0.655868846Subproblem 2
r + 0.625 = -1.280868846 Simplifying r + 0.625 = -1.280868846 Reorder the terms: 0.625 + r = -1.280868846 Solving 0.625 + r = -1.280868846 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 = -1.280868846 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + r = -1.280868846 + -0.625 r = -1.280868846 + -0.625 Combine like terms: -1.280868846 + -0.625 = -1.905868846 r = -1.905868846 Simplifying r = -1.905868846Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.655868846, -1.905868846}
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