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Simplifying r2 + -9r + -38 = -9 Reorder the terms: -38 + -9r + r2 = -9 Solving -38 + -9r + r2 = -9 Solving for variable 'r'. Reorder the terms: -38 + 9 + -9r + r2 = -9 + 9 Combine like terms: -38 + 9 = -29 -29 + -9r + r2 = -9 + 9 Combine like terms: -9 + 9 = 0 -29 + -9r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -9r + 29 + r2 = 0 + 29 Reorder the terms: -29 + 29 + -9r + r2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -9r + r2 = 0 + 29 -9r + r2 = 0 + 29 Combine like terms: 0 + 29 = 29 -9r + r2 = 29 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 = 29 + 20.25 Reorder the terms: 20.25 + -9r + r2 = 29 + 20.25 Combine like terms: 29 + 20.25 = 49.25 20.25 + -9r + r2 = 49.25 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (r + -4.5) equal to 7.017834424 and -7.017834424.Subproblem 1
r + -4.5 = 7.017834424 Simplifying r + -4.5 = 7.017834424 Reorder the terms: -4.5 + r = 7.017834424 Solving -4.5 + r = 7.017834424 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 = 7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 7.017834424 + 4.5 r = 7.017834424 + 4.5 Combine like terms: 7.017834424 + 4.5 = 11.517834424 r = 11.517834424 Simplifying r = 11.517834424Subproblem 2
r + -4.5 = -7.017834424 Simplifying r + -4.5 = -7.017834424 Reorder the terms: -4.5 + r = -7.017834424 Solving -4.5 + r = -7.017834424 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 = -7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -7.017834424 + 4.5 r = -7.017834424 + 4.5 Combine like terms: -7.017834424 + 4.5 = -2.517834424 r = -2.517834424 Simplifying r = -2.517834424Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.517834424, -2.517834424}
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