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Simplifying 0 = 6.28r2 + 1522.272r + -27346.6368 Reorder the terms: 0 = -27346.6368 + 1522.272r + 6.28r2 Solving 0 = -27346.6368 + 1522.272r + 6.28r2 Solving for variable 'r'. Combine like terms: 0 + 27346.6368 = 27346.6368 27346.6368 + -1522.272r + -6.28r2 = -27346.6368 + 1522.272r + 6.28r2 + 27346.6368 + -1522.272r + -6.28r2 Reorder the terms: 27346.6368 + -1522.272r + -6.28r2 = -27346.6368 + 27346.6368 + 1522.272r + -1522.272r + 6.28r2 + -6.28r2 Combine like terms: -27346.6368 + 27346.6368 = 0.0000 27346.6368 + -1522.272r + -6.28r2 = 0.0000 + 1522.272r + -1522.272r + 6.28r2 + -6.28r2 27346.6368 + -1522.272r + -6.28r2 = 1522.272r + -1522.272r + 6.28r2 + -6.28r2 Combine like terms: 1522.272r + -1522.272r = 0.000 27346.6368 + -1522.272r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 27346.6368 + -1522.272r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 27346.6368 + -1522.272r + -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'. -4354.56 + 242.4r + r2 = 0 Move the constant term to the right: Add '4354.56' to each side of the equation. -4354.56 + 242.4r + 4354.56 + r2 = 0 + 4354.56 Reorder the terms: -4354.56 + 4354.56 + 242.4r + r2 = 0 + 4354.56 Combine like terms: -4354.56 + 4354.56 = 0.00 0.00 + 242.4r + r2 = 0 + 4354.56 242.4r + r2 = 0 + 4354.56 Combine like terms: 0 + 4354.56 = 4354.56 242.4r + r2 = 4354.56 The r term is 242.4r. Take half its coefficient (121.2). Square it (14689.44) and add it to both sides. Add '14689.44' to each side of the equation. 242.4r + 14689.44 + r2 = 4354.56 + 14689.44 Reorder the terms: 14689.44 + 242.4r + r2 = 4354.56 + 14689.44 Combine like terms: 4354.56 + 14689.44 = 19044 14689.44 + 242.4r + r2 = 19044 Factor a perfect square on the left side: (r + 121.2)(r + 121.2) = 19044 Calculate the square root of the right side: 138 Break this problem into two subproblems by setting (r + 121.2) equal to 138 and -138.Subproblem 1
r + 121.2 = 138 Simplifying r + 121.2 = 138 Reorder the terms: 121.2 + r = 138 Solving 121.2 + r = 138 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.2' to each side of the equation. 121.2 + -121.2 + r = 138 + -121.2 Combine like terms: 121.2 + -121.2 = 0.0 0.0 + r = 138 + -121.2 r = 138 + -121.2 Combine like terms: 138 + -121.2 = 16.8 r = 16.8 Simplifying r = 16.8Subproblem 2
r + 121.2 = -138 Simplifying r + 121.2 = -138 Reorder the terms: 121.2 + r = -138 Solving 121.2 + r = -138 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.2' to each side of the equation. 121.2 + -121.2 + r = -138 + -121.2 Combine like terms: 121.2 + -121.2 = 0.0 0.0 + r = -138 + -121.2 r = -138 + -121.2 Combine like terms: -138 + -121.2 = -259.2 r = -259.2 Simplifying r = -259.2Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.8, -259.2}
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