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Simplifying 6.28(r)(r) + 62.8(r) = 603 Multiply r * r 6.28r2 + 62.8(r) = 603 Reorder the terms: 62.8r + 6.28r2 = 603 Solving 62.8r + 6.28r2 = 603 Solving for variable 'r'. Reorder the terms: -603 + 62.8r + 6.28r2 = 603 + -603 Combine like terms: 603 + -603 = 0 -603 + 62.8r + 6.28r2 = 0 Begin completing the square. Divide all terms by 6.28 the coefficient of the squared term: Divide each side by '6.28'. -96.01910828 + 10r + r2 = 0 Move the constant term to the right: Add '96.01910828' to each side of the equation. -96.01910828 + 10r + 96.01910828 + r2 = 0 + 96.01910828 Reorder the terms: -96.01910828 + 96.01910828 + 10r + r2 = 0 + 96.01910828 Combine like terms: -96.01910828 + 96.01910828 = 0.00000000 0.00000000 + 10r + r2 = 0 + 96.01910828 10r + r2 = 0 + 96.01910828 Combine like terms: 0 + 96.01910828 = 96.01910828 10r + r2 = 96.01910828 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = 96.01910828 + 25 Reorder the terms: 25 + 10r + r2 = 96.01910828 + 25 Combine like terms: 96.01910828 + 25 = 121.01910828 25 + 10r + r2 = 121.01910828 Factor a perfect square on the left side: (r + 5)(r + 5) = 121.01910828 Calculate the square root of the right side: 11.000868524 Break this problem into two subproblems by setting (r + 5) equal to 11.000868524 and -11.000868524.Subproblem 1
r + 5 = 11.000868524 Simplifying r + 5 = 11.000868524 Reorder the terms: 5 + r = 11.000868524 Solving 5 + r = 11.000868524 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 11.000868524 + -5 Combine like terms: 5 + -5 = 0 0 + r = 11.000868524 + -5 r = 11.000868524 + -5 Combine like terms: 11.000868524 + -5 = 6.000868524 r = 6.000868524 Simplifying r = 6.000868524Subproblem 2
r + 5 = -11.000868524 Simplifying r + 5 = -11.000868524 Reorder the terms: 5 + r = -11.000868524 Solving 5 + r = -11.000868524 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -11.000868524 + -5 Combine like terms: 5 + -5 = 0 0 + r = -11.000868524 + -5 r = -11.000868524 + -5 Combine like terms: -11.000868524 + -5 = -16.000868524 r = -16.000868524 Simplifying r = -16.000868524Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.000868524, -16.000868524}
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