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Simplifying 948(3r + -682) * r = 713 Reorder the terms: 948(-682 + 3r) * r = 713 Reorder the terms for easier multiplication: 948r(-682 + 3r) = 713 (-682 * 948r + 3r * 948r) = 713 (-646536r + 2844r2) = 713 Solving -646536r + 2844r2 = 713 Solving for variable 'r'. Reorder the terms: -713 + -646536r + 2844r2 = 713 + -713 Combine like terms: 713 + -713 = 0 -713 + -646536r + 2844r2 = 0 Begin completing the square. Divide all terms by 2844 the coefficient of the squared term: Divide each side by '2844'. -0.2507032349 + -227.3333333r + r2 = 0 Move the constant term to the right: Add '0.2507032349' to each side of the equation. -0.2507032349 + -227.3333333r + 0.2507032349 + r2 = 0 + 0.2507032349 Reorder the terms: -0.2507032349 + 0.2507032349 + -227.3333333r + r2 = 0 + 0.2507032349 Combine like terms: -0.2507032349 + 0.2507032349 = 0.0000000000 0.0000000000 + -227.3333333r + r2 = 0 + 0.2507032349 -227.3333333r + r2 = 0 + 0.2507032349 Combine like terms: 0 + 0.2507032349 = 0.2507032349 -227.3333333r + r2 = 0.2507032349 The r term is -227.3333333r. Take half its coefficient (-113.6666667). Square it (12920.11112) and add it to both sides. Add '12920.11112' to each side of the equation. -227.3333333r + 12920.11112 + r2 = 0.2507032349 + 12920.11112 Reorder the terms: 12920.11112 + -227.3333333r + r2 = 0.2507032349 + 12920.11112 Combine like terms: 0.2507032349 + 12920.11112 = 12920.3618232349 12920.11112 + -227.3333333r + r2 = 12920.3618232349 Factor a perfect square on the left side: (r + -113.6666667)(r + -113.6666667) = 12920.3618232349 Calculate the square root of the right side: 113.667769501 Break this problem into two subproblems by setting (r + -113.6666667) equal to 113.667769501 and -113.667769501.Subproblem 1
r + -113.6666667 = 113.667769501 Simplifying r + -113.6666667 = 113.667769501 Reorder the terms: -113.6666667 + r = 113.667769501 Solving -113.6666667 + r = 113.667769501 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '113.6666667' to each side of the equation. -113.6666667 + 113.6666667 + r = 113.667769501 + 113.6666667 Combine like terms: -113.6666667 + 113.6666667 = 0.0000000 0.0000000 + r = 113.667769501 + 113.6666667 r = 113.667769501 + 113.6666667 Combine like terms: 113.667769501 + 113.6666667 = 227.334436201 r = 227.334436201 Simplifying r = 227.334436201Subproblem 2
r + -113.6666667 = -113.667769501 Simplifying r + -113.6666667 = -113.667769501 Reorder the terms: -113.6666667 + r = -113.667769501 Solving -113.6666667 + r = -113.667769501 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '113.6666667' to each side of the equation. -113.6666667 + 113.6666667 + r = -113.667769501 + 113.6666667 Combine like terms: -113.6666667 + 113.6666667 = 0.0000000 0.0000000 + r = -113.667769501 + 113.6666667 r = -113.667769501 + 113.6666667 Combine like terms: -113.667769501 + 113.6666667 = -0.001102801 r = -0.001102801 Simplifying r = -0.001102801Solution
The solution to the problem is based on the solutions from the subproblems. r = {227.334436201, -0.001102801}
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