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Simplifying 4r2 + -3r + -2 = 0 Reorder the terms: -2 + -3r + 4r2 = 0 Solving -2 + -3r + 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'. -0.5 + -0.75r + r2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.75r + 0.5 + r2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.75r + r2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.75r + r2 = 0 + 0.5 -0.75r + r2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.75r + r2 = 0.5 The r term is -0.75r. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75r + 0.140625 + r2 = 0.5 + 0.140625 Reorder the terms: 0.140625 + -0.75r + r2 = 0.5 + 0.140625 Combine like terms: 0.5 + 0.140625 = 0.640625 0.140625 + -0.75r + r2 = 0.640625 Factor a perfect square on the left side: (r + -0.375)(r + -0.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (r + -0.375) equal to 0.80039053 and -0.80039053.Subproblem 1
r + -0.375 = 0.80039053 Simplifying r + -0.375 = 0.80039053 Reorder the terms: -0.375 + r = 0.80039053 Solving -0.375 + r = 0.80039053 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + r = 0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + r = 0.80039053 + 0.375 r = 0.80039053 + 0.375 Combine like terms: 0.80039053 + 0.375 = 1.17539053 r = 1.17539053 Simplifying r = 1.17539053Subproblem 2
r + -0.375 = -0.80039053 Simplifying r + -0.375 = -0.80039053 Reorder the terms: -0.375 + r = -0.80039053 Solving -0.375 + r = -0.80039053 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + r = -0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + r = -0.80039053 + 0.375 r = -0.80039053 + 0.375 Combine like terms: -0.80039053 + 0.375 = -0.42539053 r = -0.42539053 Simplifying r = -0.42539053Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.17539053, -0.42539053}
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