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Simplifying 100 = 50t + -0.5 * 9.81t2 Multiply -0.5 * 9.81 100 = 50t + -4.905t2 Solving 100 = 50t + -4.905t2 Solving for variable 't'. Reorder the terms: 100 + -50t + 4.905t2 = 50t + -50t + -4.905t2 + 4.905t2 Combine like terms: 50t + -50t = 0 100 + -50t + 4.905t2 = 0 + -4.905t2 + 4.905t2 100 + -50t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 100 + -50t + 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'. 20.38735984 + -10.19367992t + t2 = 0 Move the constant term to the right: Add '-20.38735984' to each side of the equation. 20.38735984 + -10.19367992t + -20.38735984 + t2 = 0 + -20.38735984 Reorder the terms: 20.38735984 + -20.38735984 + -10.19367992t + t2 = 0 + -20.38735984 Combine like terms: 20.38735984 + -20.38735984 = 0.00000000 0.00000000 + -10.19367992t + t2 = 0 + -20.38735984 -10.19367992t + t2 = 0 + -20.38735984 Combine like terms: 0 + -20.38735984 = -20.38735984 -10.19367992t + t2 = -20.38735984 The t term is -10.19367992t. Take half its coefficient (-5.09683996). Square it (25.97777758) and add it to both sides. Add '25.97777758' to each side of the equation. -10.19367992t + 25.97777758 + t2 = -20.38735984 + 25.97777758 Reorder the terms: 25.97777758 + -10.19367992t + t2 = -20.38735984 + 25.97777758 Combine like terms: -20.38735984 + 25.97777758 = 5.59041774 25.97777758 + -10.19367992t + t2 = 5.59041774 Factor a perfect square on the left side: (t + -5.09683996)(t + -5.09683996) = 5.59041774 Calculate the square root of the right side: 2.364406424 Break this problem into two subproblems by setting (t + -5.09683996) equal to 2.364406424 and -2.364406424.Subproblem 1
t + -5.09683996 = 2.364406424 Simplifying t + -5.09683996 = 2.364406424 Reorder the terms: -5.09683996 + t = 2.364406424 Solving -5.09683996 + t = 2.364406424 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.09683996' to each side of the equation. -5.09683996 + 5.09683996 + t = 2.364406424 + 5.09683996 Combine like terms: -5.09683996 + 5.09683996 = 0.00000000 0.00000000 + t = 2.364406424 + 5.09683996 t = 2.364406424 + 5.09683996 Combine like terms: 2.364406424 + 5.09683996 = 7.461246384 t = 7.461246384 Simplifying t = 7.461246384Subproblem 2
t + -5.09683996 = -2.364406424 Simplifying t + -5.09683996 = -2.364406424 Reorder the terms: -5.09683996 + t = -2.364406424 Solving -5.09683996 + t = -2.364406424 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.09683996' to each side of the equation. -5.09683996 + 5.09683996 + t = -2.364406424 + 5.09683996 Combine like terms: -5.09683996 + 5.09683996 = 0.00000000 0.00000000 + t = -2.364406424 + 5.09683996 t = -2.364406424 + 5.09683996 Combine like terms: -2.364406424 + 5.09683996 = 2.732433536 t = 2.732433536 Simplifying t = 2.732433536Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.461246384, 2.732433536}
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