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Simplifying 3r2 + -48r + 140 = 0 Reorder the terms: 140 + -48r + 3r2 = 0 Solving 140 + -48r + 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'. 46.66666667 + -16r + r2 = 0 Move the constant term to the right: Add '-46.66666667' to each side of the equation. 46.66666667 + -16r + -46.66666667 + r2 = 0 + -46.66666667 Reorder the terms: 46.66666667 + -46.66666667 + -16r + r2 = 0 + -46.66666667 Combine like terms: 46.66666667 + -46.66666667 = 0.00000000 0.00000000 + -16r + r2 = 0 + -46.66666667 -16r + r2 = 0 + -46.66666667 Combine like terms: 0 + -46.66666667 = -46.66666667 -16r + r2 = -46.66666667 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 = -46.66666667 + 64 Reorder the terms: 64 + -16r + r2 = -46.66666667 + 64 Combine like terms: -46.66666667 + 64 = 17.33333333 64 + -16r + r2 = 17.33333333 Factor a perfect square on the left side: (r + -8)(r + -8) = 17.33333333 Calculate the square root of the right side: 4.163331999 Break this problem into two subproblems by setting (r + -8) equal to 4.163331999 and -4.163331999.Subproblem 1
r + -8 = 4.163331999 Simplifying r + -8 = 4.163331999 Reorder the terms: -8 + r = 4.163331999 Solving -8 + r = 4.163331999 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 = 4.163331999 + 8 Combine like terms: -8 + 8 = 0 0 + r = 4.163331999 + 8 r = 4.163331999 + 8 Combine like terms: 4.163331999 + 8 = 12.163331999 r = 12.163331999 Simplifying r = 12.163331999Subproblem 2
r + -8 = -4.163331999 Simplifying r + -8 = -4.163331999 Reorder the terms: -8 + r = -4.163331999 Solving -8 + r = -4.163331999 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 = -4.163331999 + 8 Combine like terms: -8 + 8 = 0 0 + r = -4.163331999 + 8 r = -4.163331999 + 8 Combine like terms: -4.163331999 + 8 = 3.836668001 r = 3.836668001 Simplifying r = 3.836668001Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.163331999, 3.836668001}
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