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Simplifying 3r2 + 10r + -96 = 0 Reorder the terms: -96 + 10r + 3r2 = 0 Solving -96 + 10r + 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'. -32 + 3.333333333r + r2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 3.333333333r + 32 + r2 = 0 + 32 Reorder the terms: -32 + 32 + 3.333333333r + r2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 3.333333333r + r2 = 0 + 32 3.333333333r + r2 = 0 + 32 Combine like terms: 0 + 32 = 32 3.333333333r + r2 = 32 The r term is 3.333333333r. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333r + 2.777777779 + r2 = 32 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333r + r2 = 32 + 2.777777779 Combine like terms: 32 + 2.777777779 = 34.777777779 2.777777779 + 3.333333333r + r2 = 34.777777779 Factor a perfect square on the left side: (r + 1.666666667)(r + 1.666666667) = 34.777777779 Calculate the square root of the right side: 5.897268671 Break this problem into two subproblems by setting (r + 1.666666667) equal to 5.897268671 and -5.897268671.Subproblem 1
r + 1.666666667 = 5.897268671 Simplifying r + 1.666666667 = 5.897268671 Reorder the terms: 1.666666667 + r = 5.897268671 Solving 1.666666667 + r = 5.897268671 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + r = 5.897268671 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + r = 5.897268671 + -1.666666667 r = 5.897268671 + -1.666666667 Combine like terms: 5.897268671 + -1.666666667 = 4.230602004 r = 4.230602004 Simplifying r = 4.230602004Subproblem 2
r + 1.666666667 = -5.897268671 Simplifying r + 1.666666667 = -5.897268671 Reorder the terms: 1.666666667 + r = -5.897268671 Solving 1.666666667 + r = -5.897268671 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + r = -5.897268671 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + r = -5.897268671 + -1.666666667 r = -5.897268671 + -1.666666667 Combine like terms: -5.897268671 + -1.666666667 = -7.563935338 r = -7.563935338 Simplifying r = -7.563935338Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.230602004, -7.563935338}
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