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Simplifying 3r3 + -13r2 + -21r = 0 Reorder the terms: -21r + -13r2 + 3r3 = 0 Solving -21r + -13r2 + 3r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-21 + -13r + 3r2) = 0Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(-21 + -13r + 3r2)' equal to zero and attempt to solve: Simplifying -21 + -13r + 3r2 = 0 Solving -21 + -13r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + -4.333333333r + r2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -4.333333333r + 7 + r2 = 0 + 7 Reorder the terms: -7 + 7 + -4.333333333r + r2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4.333333333r + r2 = 0 + 7 -4.333333333r + r2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4.333333333r + r2 = 7 The r term is -4.333333333r. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333r + 4.694444446 + r2 = 7 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333r + r2 = 7 + 4.694444446 Combine like terms: 7 + 4.694444446 = 11.694444446 4.694444446 + -4.333333333r + r2 = 11.694444446 Factor a perfect square on the left side: (r + -2.166666667)(r + -2.166666667) = 11.694444446 Calculate the square root of the right side: 3.419714088 Break this problem into two subproblems by setting (r + -2.166666667) equal to 3.419714088 and -3.419714088.Subproblem 1
r + -2.166666667 = 3.419714088 Simplifying r + -2.166666667 = 3.419714088 Reorder the terms: -2.166666667 + r = 3.419714088 Solving -2.166666667 + r = 3.419714088 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + r = 3.419714088 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + r = 3.419714088 + 2.166666667 r = 3.419714088 + 2.166666667 Combine like terms: 3.419714088 + 2.166666667 = 5.586380755 r = 5.586380755 Simplifying r = 5.586380755Subproblem 2
r + -2.166666667 = -3.419714088 Simplifying r + -2.166666667 = -3.419714088 Reorder the terms: -2.166666667 + r = -3.419714088 Solving -2.166666667 + r = -3.419714088 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + r = -3.419714088 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + r = -3.419714088 + 2.166666667 r = -3.419714088 + 2.166666667 Combine like terms: -3.419714088 + 2.166666667 = -1.253047421 r = -1.253047421 Simplifying r = -1.253047421Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.586380755, -1.253047421}Solution
r = {0, 5.586380755, -1.253047421}
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