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Simplifying 25722.88 = 6.28r2 + 6.28r * 240 Reorder the terms for easier multiplication: 25722.88 = 6.28r2 + 6.28 * 240r Multiply 6.28 * 240 25722.88 = 6.28r2 + 1507.2r Reorder the terms: 25722.88 = 1507.2r + 6.28r2 Solving 25722.88 = 1507.2r + 6.28r2 Solving for variable 'r'. Reorder the terms: 25722.88 + -1507.2r + -6.28r2 = 1507.2r + -1507.2r + 6.28r2 + -6.28r2 Combine like terms: 1507.2r + -1507.2r = 0.0 25722.88 + -1507.2r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 25722.88 + -1507.2r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 25722.88 + -1507.2r + -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'. -4096 + 240r + r2 = 0 Move the constant term to the right: Add '4096' to each side of the equation. -4096 + 240r + 4096 + r2 = 0 + 4096 Reorder the terms: -4096 + 4096 + 240r + r2 = 0 + 4096 Combine like terms: -4096 + 4096 = 0 0 + 240r + r2 = 0 + 4096 240r + r2 = 0 + 4096 Combine like terms: 0 + 4096 = 4096 240r + r2 = 4096 The r term is 240r. Take half its coefficient (120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. 240r + 14400 + r2 = 4096 + 14400 Reorder the terms: 14400 + 240r + r2 = 4096 + 14400 Combine like terms: 4096 + 14400 = 18496 14400 + 240r + r2 = 18496 Factor a perfect square on the left side: (r + 120)(r + 120) = 18496 Calculate the square root of the right side: 136 Break this problem into two subproblems by setting (r + 120) equal to 136 and -136.Subproblem 1
r + 120 = 136 Simplifying r + 120 = 136 Reorder the terms: 120 + r = 136 Solving 120 + r = 136 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + r = 136 + -120 Combine like terms: 120 + -120 = 0 0 + r = 136 + -120 r = 136 + -120 Combine like terms: 136 + -120 = 16 r = 16 Simplifying r = 16Subproblem 2
r + 120 = -136 Simplifying r + 120 = -136 Reorder the terms: 120 + r = -136 Solving 120 + r = -136 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + r = -136 + -120 Combine like terms: 120 + -120 = 0 0 + r = -136 + -120 r = -136 + -120 Combine like terms: -136 + -120 = -256 r = -256 Simplifying r = -256Solution
The solution to the problem is based on the solutions from the subproblems. r = {16, -256}
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