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Simplifying r2 + 9r = 3 Reorder the terms: 9r + r2 = 3 Solving 9r + r2 = 3 Solving for variable 'r'. Reorder the terms: -3 + 9r + r2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 9r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 9r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + 9r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 9r + r2 = 0 + 3 9r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 9r + r2 = 3 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 = 3 + 20.25 Reorder the terms: 20.25 + 9r + r2 = 3 + 20.25 Combine like terms: 3 + 20.25 = 23.25 20.25 + 9r + r2 = 23.25 Factor a perfect square on the left side: (r + 4.5)(r + 4.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (r + 4.5) equal to 4.82182538 and -4.82182538.Subproblem 1
r + 4.5 = 4.82182538 Simplifying r + 4.5 = 4.82182538 Reorder the terms: 4.5 + r = 4.82182538 Solving 4.5 + r = 4.82182538 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 = 4.82182538 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = 4.82182538 + -4.5 r = 4.82182538 + -4.5 Combine like terms: 4.82182538 + -4.5 = 0.32182538 r = 0.32182538 Simplifying r = 0.32182538Subproblem 2
r + 4.5 = -4.82182538 Simplifying r + 4.5 = -4.82182538 Reorder the terms: 4.5 + r = -4.82182538 Solving 4.5 + r = -4.82182538 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 = -4.82182538 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = -4.82182538 + -4.5 r = -4.82182538 + -4.5 Combine like terms: -4.82182538 + -4.5 = -9.32182538 r = -9.32182538 Simplifying r = -9.32182538Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.32182538, -9.32182538}
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