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Simplifying 150 = 90t + -4.9t2 Solving 150 = 90t + -4.9t2 Solving for variable 't'. Reorder the terms: 150 + -90t + 4.9t2 = 90t + -90t + -4.9t2 + 4.9t2 Combine like terms: 90t + -90t = 0 150 + -90t + 4.9t2 = 0 + -4.9t2 + 4.9t2 150 + -90t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 150 + -90t + 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'. 30.6122449 + -18.36734694t + t2 = 0 Move the constant term to the right: Add '-30.6122449' to each side of the equation. 30.6122449 + -18.36734694t + -30.6122449 + t2 = 0 + -30.6122449 Reorder the terms: 30.6122449 + -30.6122449 + -18.36734694t + t2 = 0 + -30.6122449 Combine like terms: 30.6122449 + -30.6122449 = 0.0000000 0.0000000 + -18.36734694t + t2 = 0 + -30.6122449 -18.36734694t + t2 = 0 + -30.6122449 Combine like terms: 0 + -30.6122449 = -30.6122449 -18.36734694t + t2 = -30.6122449 The t term is -18.36734694t. Take half its coefficient (-9.18367347). Square it (84.33985840) and add it to both sides. Add '84.33985840' to each side of the equation. -18.36734694t + 84.33985840 + t2 = -30.6122449 + 84.33985840 Reorder the terms: 84.33985840 + -18.36734694t + t2 = -30.6122449 + 84.33985840 Combine like terms: -30.6122449 + 84.33985840 = 53.7276135 84.33985840 + -18.36734694t + t2 = 53.7276135 Factor a perfect square on the left side: (t + -9.18367347)(t + -9.18367347) = 53.7276135 Calculate the square root of the right side: 7.329912244 Break this problem into two subproblems by setting (t + -9.18367347) equal to 7.329912244 and -7.329912244.Subproblem 1
t + -9.18367347 = 7.329912244 Simplifying t + -9.18367347 = 7.329912244 Reorder the terms: -9.18367347 + t = 7.329912244 Solving -9.18367347 + t = 7.329912244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.18367347' to each side of the equation. -9.18367347 + 9.18367347 + t = 7.329912244 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + t = 7.329912244 + 9.18367347 t = 7.329912244 + 9.18367347 Combine like terms: 7.329912244 + 9.18367347 = 16.513585714 t = 16.513585714 Simplifying t = 16.513585714Subproblem 2
t + -9.18367347 = -7.329912244 Simplifying t + -9.18367347 = -7.329912244 Reorder the terms: -9.18367347 + t = -7.329912244 Solving -9.18367347 + t = -7.329912244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.18367347' to each side of the equation. -9.18367347 + 9.18367347 + t = -7.329912244 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + t = -7.329912244 + 9.18367347 t = -7.329912244 + 9.18367347 Combine like terms: -7.329912244 + 9.18367347 = 1.853761226 t = 1.853761226 Simplifying t = 1.853761226Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.513585714, 1.853761226}
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