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Simplifying -150 = 90t + -1(0.5 * 9.81t2) Multiply 0.5 * 9.81 -150 = 90t + -1(4.905t2) Remove parenthesis around (4.905t2) -150 = 90t + -1 * 4.905t2 Multiply -1 * 4.905 -150 = 90t + -4.905t2 Solving -150 = 90t + -4.905t2 Solving for variable 't'. Reorder the terms: -150 + -90t + 4.905t2 = 90t + -90t + -4.905t2 + 4.905t2 Combine like terms: 90t + -90t = 0 -150 + -90t + 4.905t2 = 0 + -4.905t2 + 4.905t2 -150 + -90t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -150 + -90t + 4.905t2 = 0.000 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -30.58103976 + -18.34862385t + t2 = 0 Move the constant term to the right: Add '30.58103976' to each side of the equation. -30.58103976 + -18.34862385t + 30.58103976 + t2 = 0 + 30.58103976 Reorder the terms: -30.58103976 + 30.58103976 + -18.34862385t + t2 = 0 + 30.58103976 Combine like terms: -30.58103976 + 30.58103976 = 0.00000000 0.00000000 + -18.34862385t + t2 = 0 + 30.58103976 -18.34862385t + t2 = 0 + 30.58103976 Combine like terms: 0 + 30.58103976 = 30.58103976 -18.34862385t + t2 = 30.58103976 The t term is -18.34862385t. Take half its coefficient (-9.174311925). Square it (84.16799930) and add it to both sides. Add '84.16799930' to each side of the equation. -18.34862385t + 84.16799930 + t2 = 30.58103976 + 84.16799930 Reorder the terms: 84.16799930 + -18.34862385t + t2 = 30.58103976 + 84.16799930 Combine like terms: 30.58103976 + 84.16799930 = 114.74903906 84.16799930 + -18.34862385t + t2 = 114.74903906 Factor a perfect square on the left side: (t + -9.174311925)(t + -9.174311925) = 114.74903906 Calculate the square root of the right side: 10.71209779 Break this problem into two subproblems by setting (t + -9.174311925) equal to 10.71209779 and -10.71209779.Subproblem 1
t + -9.174311925 = 10.71209779 Simplifying t + -9.174311925 = 10.71209779 Reorder the terms: -9.174311925 + t = 10.71209779 Solving -9.174311925 + t = 10.71209779 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.174311925' to each side of the equation. -9.174311925 + 9.174311925 + t = 10.71209779 + 9.174311925 Combine like terms: -9.174311925 + 9.174311925 = 0.000000000 0.000000000 + t = 10.71209779 + 9.174311925 t = 10.71209779 + 9.174311925 Combine like terms: 10.71209779 + 9.174311925 = 19.886409715 t = 19.886409715 Simplifying t = 19.886409715Subproblem 2
t + -9.174311925 = -10.71209779 Simplifying t + -9.174311925 = -10.71209779 Reorder the terms: -9.174311925 + t = -10.71209779 Solving -9.174311925 + t = -10.71209779 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.174311925' to each side of the equation. -9.174311925 + 9.174311925 + t = -10.71209779 + 9.174311925 Combine like terms: -9.174311925 + 9.174311925 = 0.000000000 0.000000000 + t = -10.71209779 + 9.174311925 t = -10.71209779 + 9.174311925 Combine like terms: -10.71209779 + 9.174311925 = -1.537785865 t = -1.537785865 Simplifying t = -1.537785865Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.886409715, -1.537785865}
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