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Simplifying -3r2 + -48r = -129 Reorder the terms: -48r + -3r2 = -129 Solving -48r + -3r2 = -129 Solving for variable 'r'. Reorder the terms: 129 + -48r + -3r2 = -129 + 129 Combine like terms: -129 + 129 = 0 129 + -48r + -3r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(43 + -16r + -1r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(43 + -16r + -1r2)' equal to zero and attempt to solve: Simplifying 43 + -16r + -1r2 = 0 Solving 43 + -16r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -43 + 16r + r2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + 16r + 43 + r2 = 0 + 43 Reorder the terms: -43 + 43 + 16r + r2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 16r + r2 = 0 + 43 16r + r2 = 0 + 43 Combine like terms: 0 + 43 = 43 16r + r2 = 43 The r term is 16r. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16r + 64 + r2 = 43 + 64 Reorder the terms: 64 + 16r + r2 = 43 + 64 Combine like terms: 43 + 64 = 107 64 + 16r + r2 = 107 Factor a perfect square on the left side: (r + 8)(r + 8) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (r + 8) equal to 10.344080433 and -10.344080433.Subproblem 1
r + 8 = 10.344080433 Simplifying r + 8 = 10.344080433 Reorder the terms: 8 + r = 10.344080433 Solving 8 + r = 10.344080433 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 10.344080433 + -8 Combine like terms: 8 + -8 = 0 0 + r = 10.344080433 + -8 r = 10.344080433 + -8 Combine like terms: 10.344080433 + -8 = 2.344080433 r = 2.344080433 Simplifying r = 2.344080433Subproblem 2
r + 8 = -10.344080433 Simplifying r + 8 = -10.344080433 Reorder the terms: 8 + r = -10.344080433 Solving 8 + r = -10.344080433 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -10.344080433 + -8 Combine like terms: 8 + -8 = 0 0 + r = -10.344080433 + -8 r = -10.344080433 + -8 Combine like terms: -10.344080433 + -8 = -18.344080433 r = -18.344080433 Simplifying r = -18.344080433Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.344080433, -18.344080433}Solution
r = {2.344080433, -18.344080433}
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