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Simplifying 716 = (2)(3.14) * r2 + (2)(3.14) * r(13) Multiply 2 * 3.14 716 = 6.28r2 + (2)(3.14) * r(13) Reorder the terms for easier multiplication: 716 = 6.28r2 + 2 * 3.14 * 13r Multiply 2 * 3.14 716 = 6.28r2 + 6.28 * 13r Multiply 6.28 * 13 716 = 6.28r2 + 81.64r Reorder the terms: 716 = 81.64r + 6.28r2 Solving 716 = 81.64r + 6.28r2 Solving for variable 'r'. Reorder the terms: 716 + -81.64r + -6.28r2 = 81.64r + -81.64r + 6.28r2 + -6.28r2 Combine like terms: 81.64r + -81.64r = 0.00 716 + -81.64r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 716 + -81.64r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 716 + -81.64r + -6.28r2 = 0.00 Begin completing the square. Divide all terms by -6.28 the coefficient of the squared term: Divide each side by '-6.28'. -114.0127389 + 13r + r2 = 0 Move the constant term to the right: Add '114.0127389' to each side of the equation. -114.0127389 + 13r + 114.0127389 + r2 = 0 + 114.0127389 Reorder the terms: -114.0127389 + 114.0127389 + 13r + r2 = 0 + 114.0127389 Combine like terms: -114.0127389 + 114.0127389 = 0.0000000 0.0000000 + 13r + r2 = 0 + 114.0127389 13r + r2 = 0 + 114.0127389 Combine like terms: 0 + 114.0127389 = 114.0127389 13r + r2 = 114.0127389 The r term is 13r. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13r + 42.25 + r2 = 114.0127389 + 42.25 Reorder the terms: 42.25 + 13r + r2 = 114.0127389 + 42.25 Combine like terms: 114.0127389 + 42.25 = 156.2627389 42.25 + 13r + r2 = 156.2627389 Factor a perfect square on the left side: (r + 6.5)(r + 6.5) = 156.2627389 Calculate the square root of the right side: 12.500509546 Break this problem into two subproblems by setting (r + 6.5) equal to 12.500509546 and -12.500509546.Subproblem 1
r + 6.5 = 12.500509546 Simplifying r + 6.5 = 12.500509546 Reorder the terms: 6.5 + r = 12.500509546 Solving 6.5 + r = 12.500509546 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + r = 12.500509546 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + r = 12.500509546 + -6.5 r = 12.500509546 + -6.5 Combine like terms: 12.500509546 + -6.5 = 6.000509546 r = 6.000509546 Simplifying r = 6.000509546Subproblem 2
r + 6.5 = -12.500509546 Simplifying r + 6.5 = -12.500509546 Reorder the terms: 6.5 + r = -12.500509546 Solving 6.5 + r = -12.500509546 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + r = -12.500509546 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + r = -12.500509546 + -6.5 r = -12.500509546 + -6.5 Combine like terms: -12.500509546 + -6.5 = -19.000509546 r = -19.000509546 Simplifying r = -19.000509546Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.000509546, -19.000509546}
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