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Simplifying r2 + 18r + -49 = -6 Reorder the terms: -49 + 18r + r2 = -6 Solving -49 + 18r + r2 = -6 Solving for variable 'r'. Reorder the terms: -49 + 6 + 18r + r2 = -6 + 6 Combine like terms: -49 + 6 = -43 -43 + 18r + r2 = -6 + 6 Combine like terms: -6 + 6 = 0 -43 + 18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 18r + 43 + r2 = 0 + 43 Reorder the terms: -43 + 43 + 18r + r2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 18r + r2 = 0 + 43 18r + r2 = 0 + 43 Combine like terms: 0 + 43 = 43 18r + r2 = 43 The r term is 18r. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18r + 81 + r2 = 43 + 81 Reorder the terms: 81 + 18r + r2 = 43 + 81 Combine like terms: 43 + 81 = 124 81 + 18r + r2 = 124 Factor a perfect square on the left side: (r + 9)(r + 9) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (r + 9) equal to 11.135528726 and -11.135528726.Subproblem 1
r + 9 = 11.135528726 Simplifying r + 9 = 11.135528726 Reorder the terms: 9 + r = 11.135528726 Solving 9 + r = 11.135528726 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = 11.135528726 + -9 Combine like terms: 9 + -9 = 0 0 + r = 11.135528726 + -9 r = 11.135528726 + -9 Combine like terms: 11.135528726 + -9 = 2.135528726 r = 2.135528726 Simplifying r = 2.135528726Subproblem 2
r + 9 = -11.135528726 Simplifying r + 9 = -11.135528726 Reorder the terms: 9 + r = -11.135528726 Solving 9 + r = -11.135528726 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = -11.135528726 + -9 Combine like terms: 9 + -9 = 0 0 + r = -11.135528726 + -9 r = -11.135528726 + -9 Combine like terms: -11.135528726 + -9 = -20.135528726 r = -20.135528726 Simplifying r = -20.135528726Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.135528726, -20.135528726}
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