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Simplifying -3.7 = 9.05t + -0.5 * 9.8t2 Multiply -0.5 * 9.8 -3.7 = 9.05t + -4.9t2 Solving -3.7 = 9.05t + -4.9t2 Solving for variable 't'. Reorder the terms: -3.7 + -9.05t + 4.9t2 = 9.05t + -9.05t + -4.9t2 + 4.9t2 Combine like terms: 9.05t + -9.05t = 0.00 -3.7 + -9.05t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -3.7 + -9.05t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -3.7 + -9.05t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.7551020408 + -1.846938776t + t2 = 0 Move the constant term to the right: Add '0.7551020408' to each side of the equation. -0.7551020408 + -1.846938776t + 0.7551020408 + t2 = 0 + 0.7551020408 Reorder the terms: -0.7551020408 + 0.7551020408 + -1.846938776t + t2 = 0 + 0.7551020408 Combine like terms: -0.7551020408 + 0.7551020408 = 0.0000000000 0.0000000000 + -1.846938776t + t2 = 0 + 0.7551020408 -1.846938776t + t2 = 0 + 0.7551020408 Combine like terms: 0 + 0.7551020408 = 0.7551020408 -1.846938776t + t2 = 0.7551020408 The t term is -1.846938776t. Take half its coefficient (-0.923469388). Square it (0.8527957106) and add it to both sides. Add '0.8527957106' to each side of the equation. -1.846938776t + 0.8527957106 + t2 = 0.7551020408 + 0.8527957106 Reorder the terms: 0.8527957106 + -1.846938776t + t2 = 0.7551020408 + 0.8527957106 Combine like terms: 0.7551020408 + 0.8527957106 = 1.6078977514 0.8527957106 + -1.846938776t + t2 = 1.6078977514 Factor a perfect square on the left side: (t + -0.923469388)(t + -0.923469388) = 1.6078977514 Calculate the square root of the right side: 1.268029081 Break this problem into two subproblems by setting (t + -0.923469388) equal to 1.268029081 and -1.268029081.Subproblem 1
t + -0.923469388 = 1.268029081 Simplifying t + -0.923469388 = 1.268029081 Reorder the terms: -0.923469388 + t = 1.268029081 Solving -0.923469388 + t = 1.268029081 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.923469388' to each side of the equation. -0.923469388 + 0.923469388 + t = 1.268029081 + 0.923469388 Combine like terms: -0.923469388 + 0.923469388 = 0.000000000 0.000000000 + t = 1.268029081 + 0.923469388 t = 1.268029081 + 0.923469388 Combine like terms: 1.268029081 + 0.923469388 = 2.191498469 t = 2.191498469 Simplifying t = 2.191498469Subproblem 2
t + -0.923469388 = -1.268029081 Simplifying t + -0.923469388 = -1.268029081 Reorder the terms: -0.923469388 + t = -1.268029081 Solving -0.923469388 + t = -1.268029081 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.923469388' to each side of the equation. -0.923469388 + 0.923469388 + t = -1.268029081 + 0.923469388 Combine like terms: -0.923469388 + 0.923469388 = 0.000000000 0.000000000 + t = -1.268029081 + 0.923469388 t = -1.268029081 + 0.923469388 Combine like terms: -1.268029081 + 0.923469388 = -0.344559693 t = -0.344559693 Simplifying t = -0.344559693Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.191498469, -0.344559693}
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