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Simplifying 3r2 + 9r + -4 = 0 Reorder the terms: -4 + 9r + 3r2 = 0 Solving -4 + 9r + 3r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 3r + r2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 3r + 1.333333333 + r2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 3r + r2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 3r + r2 = 0 + 1.333333333 3r + r2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 3r + r2 = 1.333333333 The r term is 3r. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3r + 2.25 + r2 = 1.333333333 + 2.25 Reorder the terms: 2.25 + 3r + r2 = 1.333333333 + 2.25 Combine like terms: 1.333333333 + 2.25 = 3.583333333 2.25 + 3r + r2 = 3.583333333 Factor a perfect square on the left side: (r + 1.5)(r + 1.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (r + 1.5) equal to 1.892969449 and -1.892969449.Subproblem 1
r + 1.5 = 1.892969449 Simplifying r + 1.5 = 1.892969449 Reorder the terms: 1.5 + r = 1.892969449 Solving 1.5 + r = 1.892969449 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = 1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 1.892969449 + -1.5 r = 1.892969449 + -1.5 Combine like terms: 1.892969449 + -1.5 = 0.392969449 r = 0.392969449 Simplifying r = 0.392969449Subproblem 2
r + 1.5 = -1.892969449 Simplifying r + 1.5 = -1.892969449 Reorder the terms: 1.5 + r = -1.892969449 Solving 1.5 + r = -1.892969449 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = -1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -1.892969449 + -1.5 r = -1.892969449 + -1.5 Combine like terms: -1.892969449 + -1.5 = -3.392969449 r = -3.392969449 Simplifying r = -3.392969449Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.392969449, -3.392969449}
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