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Simplifying 3r2 + 10r + -21 = 3 Reorder the terms: -21 + 10r + 3r2 = 3 Solving -21 + 10r + 3r2 = 3 Solving for variable 'r'. Reorder the terms: -21 + -3 + 10r + 3r2 = 3 + -3 Combine like terms: -21 + -3 = -24 -24 + 10r + 3r2 = 3 + -3 Combine like terms: 3 + -3 = 0 -24 + 10r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + 3.333333333r + r2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 3.333333333r + 8 + r2 = 0 + 8 Reorder the terms: -8 + 8 + 3.333333333r + r2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3.333333333r + r2 = 0 + 8 3.333333333r + r2 = 0 + 8 Combine like terms: 0 + 8 = 8 3.333333333r + r2 = 8 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 = 8 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333r + r2 = 8 + 2.777777779 Combine like terms: 8 + 2.777777779 = 10.777777779 2.777777779 + 3.333333333r + r2 = 10.777777779 Factor a perfect square on the left side: (r + 1.666666667)(r + 1.666666667) = 10.777777779 Calculate the square root of the right side: 3.282952601 Break this problem into two subproblems by setting (r + 1.666666667) equal to 3.282952601 and -3.282952601.Subproblem 1
r + 1.666666667 = 3.282952601 Simplifying r + 1.666666667 = 3.282952601 Reorder the terms: 1.666666667 + r = 3.282952601 Solving 1.666666667 + r = 3.282952601 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 = 3.282952601 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + r = 3.282952601 + -1.666666667 r = 3.282952601 + -1.666666667 Combine like terms: 3.282952601 + -1.666666667 = 1.616285934 r = 1.616285934 Simplifying r = 1.616285934Subproblem 2
r + 1.666666667 = -3.282952601 Simplifying r + 1.666666667 = -3.282952601 Reorder the terms: 1.666666667 + r = -3.282952601 Solving 1.666666667 + r = -3.282952601 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 = -3.282952601 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + r = -3.282952601 + -1.666666667 r = -3.282952601 + -1.666666667 Combine like terms: -3.282952601 + -1.666666667 = -4.949619268 r = -4.949619268 Simplifying r = -4.949619268Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.616285934, -4.949619268}
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