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Simplifying 5r2 + 6r + -1 = 0 Reorder the terms: -1 + 6r + 5r2 = 0 Solving -1 + 6r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 1.2r + r2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.2r + 0.2 + r2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.2r + r2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.2r + r2 = 0 + 0.2 1.2r + r2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.2r + r2 = 0.2 The r term is 1.2r. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2r + 0.36 + r2 = 0.2 + 0.36 Reorder the terms: 0.36 + 1.2r + r2 = 0.2 + 0.36 Combine like terms: 0.2 + 0.36 = 0.56 0.36 + 1.2r + r2 = 0.56 Factor a perfect square on the left side: (r + 0.6)(r + 0.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (r + 0.6) equal to 0.748331477 and -0.748331477.Subproblem 1
r + 0.6 = 0.748331477 Simplifying r + 0.6 = 0.748331477 Reorder the terms: 0.6 + r = 0.748331477 Solving 0.6 + r = 0.748331477 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + r = 0.748331477 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + r = 0.748331477 + -0.6 r = 0.748331477 + -0.6 Combine like terms: 0.748331477 + -0.6 = 0.148331477 r = 0.148331477 Simplifying r = 0.148331477Subproblem 2
r + 0.6 = -0.748331477 Simplifying r + 0.6 = -0.748331477 Reorder the terms: 0.6 + r = -0.748331477 Solving 0.6 + r = -0.748331477 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + r = -0.748331477 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + r = -0.748331477 + -0.6 r = -0.748331477 + -0.6 Combine like terms: -0.748331477 + -0.6 = -1.348331477 r = -1.348331477 Simplifying r = -1.348331477Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.148331477, -1.348331477}
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