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Simplifying 3620 + 47.88t + -4.9t2 = 0 Solving 3620 + 47.88t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -738.7755102 + -9.771428571t + t2 = 0 Move the constant term to the right: Add '738.7755102' to each side of the equation. -738.7755102 + -9.771428571t + 738.7755102 + t2 = 0 + 738.7755102 Reorder the terms: -738.7755102 + 738.7755102 + -9.771428571t + t2 = 0 + 738.7755102 Combine like terms: -738.7755102 + 738.7755102 = 0.0000000 0.0000000 + -9.771428571t + t2 = 0 + 738.7755102 -9.771428571t + t2 = 0 + 738.7755102 Combine like terms: 0 + 738.7755102 = 738.7755102 -9.771428571t + t2 = 738.7755102 The t term is -9.771428571t. Take half its coefficient (-4.885714286). Square it (23.87020408) and add it to both sides. Add '23.87020408' to each side of the equation. -9.771428571t + 23.87020408 + t2 = 738.7755102 + 23.87020408 Reorder the terms: 23.87020408 + -9.771428571t + t2 = 738.7755102 + 23.87020408 Combine like terms: 738.7755102 + 23.87020408 = 762.64571428 23.87020408 + -9.771428571t + t2 = 762.64571428 Factor a perfect square on the left side: (t + -4.885714286)(t + -4.885714286) = 762.64571428 Calculate the square root of the right side: 27.616040887 Break this problem into two subproblems by setting (t + -4.885714286) equal to 27.616040887 and -27.616040887.Subproblem 1
t + -4.885714286 = 27.616040887 Simplifying t + -4.885714286 = 27.616040887 Reorder the terms: -4.885714286 + t = 27.616040887 Solving -4.885714286 + t = 27.616040887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.885714286' to each side of the equation. -4.885714286 + 4.885714286 + t = 27.616040887 + 4.885714286 Combine like terms: -4.885714286 + 4.885714286 = 0.000000000 0.000000000 + t = 27.616040887 + 4.885714286 t = 27.616040887 + 4.885714286 Combine like terms: 27.616040887 + 4.885714286 = 32.501755173 t = 32.501755173 Simplifying t = 32.501755173Subproblem 2
t + -4.885714286 = -27.616040887 Simplifying t + -4.885714286 = -27.616040887 Reorder the terms: -4.885714286 + t = -27.616040887 Solving -4.885714286 + t = -27.616040887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.885714286' to each side of the equation. -4.885714286 + 4.885714286 + t = -27.616040887 + 4.885714286 Combine like terms: -4.885714286 + 4.885714286 = 0.000000000 0.000000000 + t = -27.616040887 + 4.885714286 t = -27.616040887 + 4.885714286 Combine like terms: -27.616040887 + 4.885714286 = -22.730326601 t = -22.730326601 Simplifying t = -22.730326601Solution
The solution to the problem is based on the solutions from the subproblems. t = {32.501755173, -22.730326601}
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