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Simplifying 9360 + 624t + -4.9t2 = 0 Solving 9360 + 624t + -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'. -1910.204082 + -127.3469388t + t2 = 0 Move the constant term to the right: Add '1910.204082' to each side of the equation. -1910.204082 + -127.3469388t + 1910.204082 + t2 = 0 + 1910.204082 Reorder the terms: -1910.204082 + 1910.204082 + -127.3469388t + t2 = 0 + 1910.204082 Combine like terms: -1910.204082 + 1910.204082 = 0.000000 0.000000 + -127.3469388t + t2 = 0 + 1910.204082 -127.3469388t + t2 = 0 + 1910.204082 Combine like terms: 0 + 1910.204082 = 1910.204082 -127.3469388t + t2 = 1910.204082 The t term is -127.3469388t. Take half its coefficient (-63.6734694). Square it (4054.310705) and add it to both sides. Add '4054.310705' to each side of the equation. -127.3469388t + 4054.310705 + t2 = 1910.204082 + 4054.310705 Reorder the terms: 4054.310705 + -127.3469388t + t2 = 1910.204082 + 4054.310705 Combine like terms: 1910.204082 + 4054.310705 = 5964.514787 4054.310705 + -127.3469388t + t2 = 5964.514787 Factor a perfect square on the left side: (t + -63.6734694)(t + -63.6734694) = 5964.514787 Calculate the square root of the right side: 77.230271183 Break this problem into two subproblems by setting (t + -63.6734694) equal to 77.230271183 and -77.230271183.Subproblem 1
t + -63.6734694 = 77.230271183 Simplifying t + -63.6734694 = 77.230271183 Reorder the terms: -63.6734694 + t = 77.230271183 Solving -63.6734694 + t = 77.230271183 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '63.6734694' to each side of the equation. -63.6734694 + 63.6734694 + t = 77.230271183 + 63.6734694 Combine like terms: -63.6734694 + 63.6734694 = 0.0000000 0.0000000 + t = 77.230271183 + 63.6734694 t = 77.230271183 + 63.6734694 Combine like terms: 77.230271183 + 63.6734694 = 140.903740583 t = 140.903740583 Simplifying t = 140.903740583Subproblem 2
t + -63.6734694 = -77.230271183 Simplifying t + -63.6734694 = -77.230271183 Reorder the terms: -63.6734694 + t = -77.230271183 Solving -63.6734694 + t = -77.230271183 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '63.6734694' to each side of the equation. -63.6734694 + 63.6734694 + t = -77.230271183 + 63.6734694 Combine like terms: -63.6734694 + 63.6734694 = 0.0000000 0.0000000 + t = -77.230271183 + 63.6734694 t = -77.230271183 + 63.6734694 Combine like terms: -77.230271183 + 63.6734694 = -13.556801783 t = -13.556801783 Simplifying t = -13.556801783Solution
The solution to the problem is based on the solutions from the subproblems. t = {140.903740583, -13.556801783}
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