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Simplifying 3r2 + 12r + -1 = 0 Reorder the terms: -1 + 12r + 3r2 = 0 Solving -1 + 12r + 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'. -0.3333333333 + 4r + r2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 4r + 0.3333333333 + r2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 4r + r2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 4r + r2 = 0 + 0.3333333333 4r + r2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 4r + r2 = 0.3333333333 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 0.3333333333 + 4 Reorder the terms: 4 + 4r + r2 = 0.3333333333 + 4 Combine like terms: 0.3333333333 + 4 = 4.3333333333 4 + 4r + r2 = 4.3333333333 Factor a perfect square on the left side: (r + 2)(r + 2) = 4.3333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (r + 2) equal to 2.081665999 and -2.081665999.Subproblem 1
r + 2 = 2.081665999 Simplifying r + 2 = 2.081665999 Reorder the terms: 2 + r = 2.081665999 Solving 2 + r = 2.081665999 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + r = 2.081665999 + -2 r = 2.081665999 + -2 Combine like terms: 2.081665999 + -2 = 0.081665999 r = 0.081665999 Simplifying r = 0.081665999Subproblem 2
r + 2 = -2.081665999 Simplifying r + 2 = -2.081665999 Reorder the terms: 2 + r = -2.081665999 Solving 2 + r = -2.081665999 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + r = -2.081665999 + -2 r = -2.081665999 + -2 Combine like terms: -2.081665999 + -2 = -4.081665999 r = -4.081665999 Simplifying r = -4.081665999Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.081665999, -4.081665999}
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