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Simplifying 13602.48 = 2 * 3.14r2 + 2r * 95 Multiply 2 * 3.14 13602.48 = 6.28r2 + 2r * 95 Reorder the terms for easier multiplication: 13602.48 = 6.28r2 + 2 * 95r Multiply 2 * 95 13602.48 = 6.28r2 + 190r Reorder the terms: 13602.48 = 190r + 6.28r2 Solving 13602.48 = 190r + 6.28r2 Solving for variable 'r'. Reorder the terms: 13602.48 + -190r + -6.28r2 = 190r + -190r + 6.28r2 + -6.28r2 Combine like terms: 190r + -190r = 0 13602.48 + -190r + -6.28r2 = 0 + 6.28r2 + -6.28r2 13602.48 + -190r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 13602.48 + -190r + -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'. -2166 + 30.25477707r + r2 = 0 Move the constant term to the right: Add '2166' to each side of the equation. -2166 + 30.25477707r + 2166 + r2 = 0 + 2166 Reorder the terms: -2166 + 2166 + 30.25477707r + r2 = 0 + 2166 Combine like terms: -2166 + 2166 = 0 0 + 30.25477707r + r2 = 0 + 2166 30.25477707r + r2 = 0 + 2166 Combine like terms: 0 + 2166 = 2166 30.25477707r + r2 = 2166 The r term is 30.25477707r. Take half its coefficient (15.12738854). Square it (228.8378840) and add it to both sides. Add '228.8378840' to each side of the equation. 30.25477707r + 228.8378840 + r2 = 2166 + 228.8378840 Reorder the terms: 228.8378840 + 30.25477707r + r2 = 2166 + 228.8378840 Combine like terms: 2166 + 228.8378840 = 2394.837884 228.8378840 + 30.25477707r + r2 = 2394.837884 Factor a perfect square on the left side: (r + 15.12738854)(r + 15.12738854) = 2394.837884 Calculate the square root of the right side: 48.937080869 Break this problem into two subproblems by setting (r + 15.12738854) equal to 48.937080869 and -48.937080869.Subproblem 1
r + 15.12738854 = 48.937080869 Simplifying r + 15.12738854 = 48.937080869 Reorder the terms: 15.12738854 + r = 48.937080869 Solving 15.12738854 + r = 48.937080869 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15.12738854' to each side of the equation. 15.12738854 + -15.12738854 + r = 48.937080869 + -15.12738854 Combine like terms: 15.12738854 + -15.12738854 = 0.00000000 0.00000000 + r = 48.937080869 + -15.12738854 r = 48.937080869 + -15.12738854 Combine like terms: 48.937080869 + -15.12738854 = 33.809692329 r = 33.809692329 Simplifying r = 33.809692329Subproblem 2
r + 15.12738854 = -48.937080869 Simplifying r + 15.12738854 = -48.937080869 Reorder the terms: 15.12738854 + r = -48.937080869 Solving 15.12738854 + r = -48.937080869 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15.12738854' to each side of the equation. 15.12738854 + -15.12738854 + r = -48.937080869 + -15.12738854 Combine like terms: 15.12738854 + -15.12738854 = 0.00000000 0.00000000 + r = -48.937080869 + -15.12738854 r = -48.937080869 + -15.12738854 Combine like terms: -48.937080869 + -15.12738854 = -64.064469409 r = -64.064469409 Simplifying r = -64.064469409Solution
The solution to the problem is based on the solutions from the subproblems. r = {33.809692329, -64.064469409}
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