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Simplifying r2 + 10r = 9 Reorder the terms: 10r + r2 = 9 Solving 10r + r2 = 9 Solving for variable 'r'. Reorder the terms: -9 + 10r + r2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + 10r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10r + r2 = 0 + 9 10r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 10r + r2 = 9 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = 9 + 25 Reorder the terms: 25 + 10r + r2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10r + r2 = 34 Factor a perfect square on the left side: (r + 5)(r + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (r + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
r + 5 = 5.830951895 Simplifying r + 5 = 5.830951895 Reorder the terms: 5 + r = 5.830951895 Solving 5 + r = 5.830951895 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + r = 5.830951895 + -5 r = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 r = 0.830951895 Simplifying r = 0.830951895Subproblem 2
r + 5 = -5.830951895 Simplifying r + 5 = -5.830951895 Reorder the terms: 5 + r = -5.830951895 Solving 5 + r = -5.830951895 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + r = -5.830951895 + -5 r = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 r = -10.830951895 Simplifying r = -10.830951895Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.830951895, -10.830951895}
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