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Simplifying r2 + -23r + -10 = 0 Reorder the terms: -10 + -23r + r2 = 0 Solving -10 + -23r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -23r + 10 + r2 = 0 + 10 Reorder the terms: -10 + 10 + -23r + r2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -23r + r2 = 0 + 10 -23r + r2 = 0 + 10 Combine like terms: 0 + 10 = 10 -23r + r2 = 10 The r term is -23r. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23r + 132.25 + r2 = 10 + 132.25 Reorder the terms: 132.25 + -23r + r2 = 10 + 132.25 Combine like terms: 10 + 132.25 = 142.25 132.25 + -23r + r2 = 142.25 Factor a perfect square on the left side: (r + -11.5)(r + -11.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (r + -11.5) equal to 11.926860442 and -11.926860442.Subproblem 1
r + -11.5 = 11.926860442 Simplifying r + -11.5 = 11.926860442 Reorder the terms: -11.5 + r = 11.926860442 Solving -11.5 + r = 11.926860442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + r = 11.926860442 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + r = 11.926860442 + 11.5 r = 11.926860442 + 11.5 Combine like terms: 11.926860442 + 11.5 = 23.426860442 r = 23.426860442 Simplifying r = 23.426860442Subproblem 2
r + -11.5 = -11.926860442 Simplifying r + -11.5 = -11.926860442 Reorder the terms: -11.5 + r = -11.926860442 Solving -11.5 + r = -11.926860442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + r = -11.926860442 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + r = -11.926860442 + 11.5 r = -11.926860442 + 11.5 Combine like terms: -11.926860442 + 11.5 = -0.426860442 r = -0.426860442 Simplifying r = -0.426860442Solution
The solution to the problem is based on the solutions from the subproblems. r = {23.426860442, -0.426860442}
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