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Simplifying 3r2 + 8r = 21 Reorder the terms: 8r + 3r2 = 21 Solving 8r + 3r2 = 21 Solving for variable 'r'. Reorder the terms: -21 + 8r + 3r2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 8r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + 2.666666667r + r2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 2.666666667r + 7 + r2 = 0 + 7 Reorder the terms: -7 + 7 + 2.666666667r + r2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2.666666667r + r2 = 0 + 7 2.666666667r + r2 = 0 + 7 Combine like terms: 0 + 7 = 7 2.666666667r + r2 = 7 The r term is 2.666666667r. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667r + 1.777777780 + r2 = 7 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667r + r2 = 7 + 1.777777780 Combine like terms: 7 + 1.777777780 = 8.77777778 1.777777780 + 2.666666667r + r2 = 8.77777778 Factor a perfect square on the left side: (r + 1.333333334)(r + 1.333333334) = 8.77777778 Calculate the square root of the right side: 2.962731473 Break this problem into two subproblems by setting (r + 1.333333334) equal to 2.962731473 and -2.962731473.Subproblem 1
r + 1.333333334 = 2.962731473 Simplifying r + 1.333333334 = 2.962731473 Reorder the terms: 1.333333334 + r = 2.962731473 Solving 1.333333334 + r = 2.962731473 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + r = 2.962731473 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + r = 2.962731473 + -1.333333334 r = 2.962731473 + -1.333333334 Combine like terms: 2.962731473 + -1.333333334 = 1.629398139 r = 1.629398139 Simplifying r = 1.629398139Subproblem 2
r + 1.333333334 = -2.962731473 Simplifying r + 1.333333334 = -2.962731473 Reorder the terms: 1.333333334 + r = -2.962731473 Solving 1.333333334 + r = -2.962731473 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + r = -2.962731473 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + r = -2.962731473 + -1.333333334 r = -2.962731473 + -1.333333334 Combine like terms: -2.962731473 + -1.333333334 = -4.296064807 r = -4.296064807 Simplifying r = -4.296064807Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.629398139, -4.296064807}
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