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Simplifying 3r2 + -12r + 4 = 0 Reorder the terms: 4 + -12r + 3r2 = 0 Solving 4 + -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'. 1.333333333 + -4r + r2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -4r + -1.333333333 + r2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -4r + r2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -4r + r2 = 0 + -1.333333333 -4r + r2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -4r + r2 = -1.333333333 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 = -1.333333333 + 4 Reorder the terms: 4 + -4r + r2 = -1.333333333 + 4 Combine like terms: -1.333333333 + 4 = 2.666666667 4 + -4r + r2 = 2.666666667 Factor a perfect square on the left side: (r + -2)(r + -2) = 2.666666667 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (r + -2) equal to 1.632993162 and -1.632993162.Subproblem 1
r + -2 = 1.632993162 Simplifying r + -2 = 1.632993162 Reorder the terms: -2 + r = 1.632993162 Solving -2 + r = 1.632993162 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 = 1.632993162 + 2 Combine like terms: -2 + 2 = 0 0 + r = 1.632993162 + 2 r = 1.632993162 + 2 Combine like terms: 1.632993162 + 2 = 3.632993162 r = 3.632993162 Simplifying r = 3.632993162Subproblem 2
r + -2 = -1.632993162 Simplifying r + -2 = -1.632993162 Reorder the terms: -2 + r = -1.632993162 Solving -2 + r = -1.632993162 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 = -1.632993162 + 2 Combine like terms: -2 + 2 = 0 0 + r = -1.632993162 + 2 r = -1.632993162 + 2 Combine like terms: -1.632993162 + 2 = 0.367006838 r = 0.367006838 Simplifying r = 0.367006838Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.632993162, 0.367006838}
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