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Simplifying 4 + -3r2 = -12r Solving 4 + -3r2 = -12r Solving for variable 'r'. Reorder the terms: 4 + 12r + -3r2 = -12r + 12r Combine like terms: -12r + 12r = 0 4 + 12r + -3r2 = 0 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 = 5.333333333 4 + -4r + r2 = 5.333333333 Factor a perfect square on the left side: (r + -2)(r + -2) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (r + -2) equal to 2.309401077 and -2.309401077.Subproblem 1
r + -2 = 2.309401077 Simplifying r + -2 = 2.309401077 Reorder the terms: -2 + r = 2.309401077 Solving -2 + r = 2.309401077 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 = 2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.309401077 + 2 r = 2.309401077 + 2 Combine like terms: 2.309401077 + 2 = 4.309401077 r = 4.309401077 Simplifying r = 4.309401077Subproblem 2
r + -2 = -2.309401077 Simplifying r + -2 = -2.309401077 Reorder the terms: -2 + r = -2.309401077 Solving -2 + r = -2.309401077 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 = -2.309401077 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.309401077 + 2 r = -2.309401077 + 2 Combine like terms: -2.309401077 + 2 = -0.309401077 r = -0.309401077 Simplifying r = -0.309401077Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.309401077, -0.309401077}
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