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Simplifying r2 + 15r + 50 = 9 Reorder the terms: 50 + 15r + r2 = 9 Solving 50 + 15r + r2 = 9 Solving for variable 'r'. Reorder the terms: 50 + -9 + 15r + r2 = 9 + -9 Combine like terms: 50 + -9 = 41 41 + 15r + r2 = 9 + -9 Combine like terms: 9 + -9 = 0 41 + 15r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 15r + -41 + r2 = 0 + -41 Reorder the terms: 41 + -41 + 15r + r2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 15r + r2 = 0 + -41 15r + r2 = 0 + -41 Combine like terms: 0 + -41 = -41 15r + r2 = -41 The r term is 15r. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15r + 56.25 + r2 = -41 + 56.25 Reorder the terms: 56.25 + 15r + r2 = -41 + 56.25 Combine like terms: -41 + 56.25 = 15.25 56.25 + 15r + r2 = 15.25 Factor a perfect square on the left side: (r + 7.5)(r + 7.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (r + 7.5) equal to 3.905124838 and -3.905124838.Subproblem 1
r + 7.5 = 3.905124838 Simplifying r + 7.5 = 3.905124838 Reorder the terms: 7.5 + r = 3.905124838 Solving 7.5 + r = 3.905124838 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = 3.905124838 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = 3.905124838 + -7.5 r = 3.905124838 + -7.5 Combine like terms: 3.905124838 + -7.5 = -3.594875162 r = -3.594875162 Simplifying r = -3.594875162Subproblem 2
r + 7.5 = -3.905124838 Simplifying r + 7.5 = -3.905124838 Reorder the terms: 7.5 + r = -3.905124838 Solving 7.5 + r = -3.905124838 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = -3.905124838 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = -3.905124838 + -7.5 r = -3.905124838 + -7.5 Combine like terms: -3.905124838 + -7.5 = -11.405124838 r = -11.405124838 Simplifying r = -11.405124838Solution
The solution to the problem is based on the solutions from the subproblems. r = {-3.594875162, -11.405124838}
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