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Simplifying r(r + 11) + -88 = 0 Reorder the terms: r(11 + r) + -88 = 0 (11 * r + r * r) + -88 = 0 (11r + r2) + -88 = 0 Reorder the terms: -88 + 11r + r2 = 0 Solving -88 + 11r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 11r + 88 + r2 = 0 + 88 Reorder the terms: -88 + 88 + 11r + r2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 11r + r2 = 0 + 88 11r + r2 = 0 + 88 Combine like terms: 0 + 88 = 88 11r + r2 = 88 The r term is 11r. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11r + 30.25 + r2 = 88 + 30.25 Reorder the terms: 30.25 + 11r + r2 = 88 + 30.25 Combine like terms: 88 + 30.25 = 118.25 30.25 + 11r + r2 = 118.25 Factor a perfect square on the left side: (r + 5.5)(r + 5.5) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (r + 5.5) equal to 10.874281585 and -10.874281585.Subproblem 1
r + 5.5 = 10.874281585 Simplifying r + 5.5 = 10.874281585 Reorder the terms: 5.5 + r = 10.874281585 Solving 5.5 + r = 10.874281585 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + r = 10.874281585 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + r = 10.874281585 + -5.5 r = 10.874281585 + -5.5 Combine like terms: 10.874281585 + -5.5 = 5.374281585 r = 5.374281585 Simplifying r = 5.374281585Subproblem 2
r + 5.5 = -10.874281585 Simplifying r + 5.5 = -10.874281585 Reorder the terms: 5.5 + r = -10.874281585 Solving 5.5 + r = -10.874281585 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + r = -10.874281585 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + r = -10.874281585 + -5.5 r = -10.874281585 + -5.5 Combine like terms: -10.874281585 + -5.5 = -16.374281585 r = -16.374281585 Simplifying r = -16.374281585Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.374281585, -16.374281585}
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