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Simplifying -2r2 + 8r = -5 Reorder the terms: 8r + -2r2 = -5 Solving 8r + -2r2 = -5 Solving for variable 'r'. Reorder the terms: 5 + 8r + -2r2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 8r + -2r2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -4r + r2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -4r + 2.5 + r2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -4r + r2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -4r + r2 = 0 + 2.5 -4r + r2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -4r + r2 = 2.5 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 2.5 + 4 Reorder the terms: 4 + -4r + r2 = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 4 + -4r + r2 = 6.5 Factor a perfect square on the left side: (r + -2)(r + -2) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (r + -2) equal to 2.549509757 and -2.549509757.Subproblem 1
r + -2 = 2.549509757 Simplifying r + -2 = 2.549509757 Reorder the terms: -2 + r = 2.549509757 Solving -2 + r = 2.549509757 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.549509757 + 2 r = 2.549509757 + 2 Combine like terms: 2.549509757 + 2 = 4.549509757 r = 4.549509757 Simplifying r = 4.549509757Subproblem 2
r + -2 = -2.549509757 Simplifying r + -2 = -2.549509757 Reorder the terms: -2 + r = -2.549509757 Solving -2 + r = -2.549509757 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.549509757 + 2 r = -2.549509757 + 2 Combine like terms: -2.549509757 + 2 = -0.549509757 r = -0.549509757 Simplifying r = -0.549509757Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.549509757, -0.549509757}
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