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Simplifying 750 = 2(3.14)(r * r) + 2(3.14) * r(50) Multiply r * r 750 = 2 * 3.14(r2) + 2(3.14) * r(50) Multiply 2 * 3.14 750 = 6.28r2 + 2(3.14) * r(50) Reorder the terms for easier multiplication: 750 = 6.28r2 + 2 * 3.14 * 50r Multiply 2 * 3.14 750 = 6.28r2 + 6.28 * 50r Multiply 6.28 * 50 750 = 6.28r2 + 314r Reorder the terms: 750 = 314r + 6.28r2 Solving 750 = 314r + 6.28r2 Solving for variable 'r'. Reorder the terms: 750 + -314r + -6.28r2 = 314r + -314r + 6.28r2 + -6.28r2 Combine like terms: 314r + -314r = 0 750 + -314r + -6.28r2 = 0 + 6.28r2 + -6.28r2 750 + -314r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 750 + -314r + -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'. -119.4267516 + 50r + r2 = 0 Move the constant term to the right: Add '119.4267516' to each side of the equation. -119.4267516 + 50r + 119.4267516 + r2 = 0 + 119.4267516 Reorder the terms: -119.4267516 + 119.4267516 + 50r + r2 = 0 + 119.4267516 Combine like terms: -119.4267516 + 119.4267516 = 0.0000000 0.0000000 + 50r + r2 = 0 + 119.4267516 50r + r2 = 0 + 119.4267516 Combine like terms: 0 + 119.4267516 = 119.4267516 50r + r2 = 119.4267516 The r term is 50r. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50r + 625 + r2 = 119.4267516 + 625 Reorder the terms: 625 + 50r + r2 = 119.4267516 + 625 Combine like terms: 119.4267516 + 625 = 744.4267516 625 + 50r + r2 = 744.4267516 Factor a perfect square on the left side: (r + 25)(r + 25) = 744.4267516 Calculate the square root of the right side: 27.284185009 Break this problem into two subproblems by setting (r + 25) equal to 27.284185009 and -27.284185009.Subproblem 1
r + 25 = 27.284185009 Simplifying r + 25 = 27.284185009 Reorder the terms: 25 + r = 27.284185009 Solving 25 + r = 27.284185009 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + r = 27.284185009 + -25 Combine like terms: 25 + -25 = 0 0 + r = 27.284185009 + -25 r = 27.284185009 + -25 Combine like terms: 27.284185009 + -25 = 2.284185009 r = 2.284185009 Simplifying r = 2.284185009Subproblem 2
r + 25 = -27.284185009 Simplifying r + 25 = -27.284185009 Reorder the terms: 25 + r = -27.284185009 Solving 25 + r = -27.284185009 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + r = -27.284185009 + -25 Combine like terms: 25 + -25 = 0 0 + r = -27.284185009 + -25 r = -27.284185009 + -25 Combine like terms: -27.284185009 + -25 = -52.284185009 r = -52.284185009 Simplifying r = -52.284185009Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.284185009, -52.284185009}
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