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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 = 114.9521033 84.33985840 + -18.36734694t + t2 = 114.9521033 Factor a perfect square on the left side: (t + -9.18367347)(t + -9.18367347) = 114.9521033 Calculate the square root of the right side: 10.721571867 Break this problem into two subproblems by setting (t + -9.18367347) equal to 10.721571867 and -10.721571867.Subproblem 1
t + -9.18367347 = 10.721571867 Simplifying t + -9.18367347 = 10.721571867 Reorder the terms: -9.18367347 + t = 10.721571867 Solving -9.18367347 + t = 10.721571867 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 = 10.721571867 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + t = 10.721571867 + 9.18367347 t = 10.721571867 + 9.18367347 Combine like terms: 10.721571867 + 9.18367347 = 19.905245337 t = 19.905245337 Simplifying t = 19.905245337Subproblem 2
t + -9.18367347 = -10.721571867 Simplifying t + -9.18367347 = -10.721571867 Reorder the terms: -9.18367347 + t = -10.721571867 Solving -9.18367347 + t = -10.721571867 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 = -10.721571867 + 9.18367347 Combine like terms: -9.18367347 + 9.18367347 = 0.00000000 0.00000000 + t = -10.721571867 + 9.18367347 t = -10.721571867 + 9.18367347 Combine like terms: -10.721571867 + 9.18367347 = -1.537898397 t = -1.537898397 Simplifying t = -1.537898397Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.905245337, -1.537898397}
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