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Simplifying -2r2 + 2r + 5 = 0 Reorder the terms: 5 + 2r + -2r2 = 0 Solving 5 + 2r + -2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -1r + r2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1r + 2.5 + r2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1r + r2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1r + r2 = 0 + 2.5 -1r + r2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1r + r2 = 2.5 The r term is -1r. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = 2.5 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + -1r + r2 = 2.75 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (r + -0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
r + -0.5 = 1.658312395 Simplifying r + -0.5 = 1.658312395 Reorder the terms: -0.5 + r = 1.658312395 Solving -0.5 + r = 1.658312395 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 1.658312395 + 0.5 r = 1.658312395 + 0.5 Combine like terms: 1.658312395 + 0.5 = 2.158312395 r = 2.158312395 Simplifying r = 2.158312395Subproblem 2
r + -0.5 = -1.658312395 Simplifying r + -0.5 = -1.658312395 Reorder the terms: -0.5 + r = -1.658312395 Solving -0.5 + r = -1.658312395 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -1.658312395 + 0.5 r = -1.658312395 + 0.5 Combine like terms: -1.658312395 + 0.5 = -1.158312395 r = -1.158312395 Simplifying r = -1.158312395Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.158312395, -1.158312395}
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