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Simplifying r2 + 9r = 80 Reorder the terms: 9r + r2 = 80 Solving 9r + r2 = 80 Solving for variable 'r'. Reorder the terms: -80 + 9r + r2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 9r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 9r + 80 + r2 = 0 + 80 Reorder the terms: -80 + 80 + 9r + r2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 9r + r2 = 0 + 80 9r + r2 = 0 + 80 Combine like terms: 0 + 80 = 80 9r + r2 = 80 The r term is 9r. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9r + 20.25 + r2 = 80 + 20.25 Reorder the terms: 20.25 + 9r + r2 = 80 + 20.25 Combine like terms: 80 + 20.25 = 100.25 20.25 + 9r + r2 = 100.25 Factor a perfect square on the left side: (r + 4.5)(r + 4.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (r + 4.5) equal to 10.012492197 and -10.012492197.Subproblem 1
r + 4.5 = 10.012492197 Simplifying r + 4.5 = 10.012492197 Reorder the terms: 4.5 + r = 10.012492197 Solving 4.5 + r = 10.012492197 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + r = 10.012492197 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = 10.012492197 + -4.5 r = 10.012492197 + -4.5 Combine like terms: 10.012492197 + -4.5 = 5.512492197 r = 5.512492197 Simplifying r = 5.512492197Subproblem 2
r + 4.5 = -10.012492197 Simplifying r + 4.5 = -10.012492197 Reorder the terms: 4.5 + r = -10.012492197 Solving 4.5 + r = -10.012492197 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + r = -10.012492197 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = -10.012492197 + -4.5 r = -10.012492197 + -4.5 Combine like terms: -10.012492197 + -4.5 = -14.512492197 r = -14.512492197 Simplifying r = -14.512492197Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.512492197, -14.512492197}
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