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Simplifying 6611.584 = 6.28r2 + 384.336r Reorder the terms: 6611.584 = 384.336r + 6.28r2 Solving 6611.584 = 384.336r + 6.28r2 Solving for variable 'r'. Reorder the terms: 6611.584 + -384.336r + -6.28r2 = 384.336r + -384.336r + 6.28r2 + -6.28r2 Combine like terms: 384.336r + -384.336r = 0.000 6611.584 + -384.336r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 6611.584 + -384.336r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 6611.584 + -384.336r + -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'. -1052.8 + 61.2r + r2 = 0 Move the constant term to the right: Add '1052.8' to each side of the equation. -1052.8 + 61.2r + 1052.8 + r2 = 0 + 1052.8 Reorder the terms: -1052.8 + 1052.8 + 61.2r + r2 = 0 + 1052.8 Combine like terms: -1052.8 + 1052.8 = 0.0 0.0 + 61.2r + r2 = 0 + 1052.8 61.2r + r2 = 0 + 1052.8 Combine like terms: 0 + 1052.8 = 1052.8 61.2r + r2 = 1052.8 The r term is 61.2r. Take half its coefficient (30.6). Square it (936.36) and add it to both sides. Add '936.36' to each side of the equation. 61.2r + 936.36 + r2 = 1052.8 + 936.36 Reorder the terms: 936.36 + 61.2r + r2 = 1052.8 + 936.36 Combine like terms: 1052.8 + 936.36 = 1989.16 936.36 + 61.2r + r2 = 1989.16 Factor a perfect square on the left side: (r + 30.6)(r + 30.6) = 1989.16 Calculate the square root of the right side: 44.6 Break this problem into two subproblems by setting (r + 30.6) equal to 44.6 and -44.6.Subproblem 1
r + 30.6 = 44.6 Simplifying r + 30.6 = 44.6 Reorder the terms: 30.6 + r = 44.6 Solving 30.6 + r = 44.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-30.6' to each side of the equation. 30.6 + -30.6 + r = 44.6 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 0.0 + r = 44.6 + -30.6 r = 44.6 + -30.6 Combine like terms: 44.6 + -30.6 = 14 r = 14 Simplifying r = 14Subproblem 2
r + 30.6 = -44.6 Simplifying r + 30.6 = -44.6 Reorder the terms: 30.6 + r = -44.6 Solving 30.6 + r = -44.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-30.6' to each side of the equation. 30.6 + -30.6 + r = -44.6 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 0.0 + r = -44.6 + -30.6 r = -44.6 + -30.6 Combine like terms: -44.6 + -30.6 = -75.2 r = -75.2 Simplifying r = -75.2Solution
The solution to the problem is based on the solutions from the subproblems. r = {14, -75.2}
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