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Simplifying -109 = (37.2615t) + -4.9t2 Solving -109 = (37.2615t) + -4.9t2 Solving for variable 't'. Reorder the terms: -109 + (-37.2615t) + 4.9t2 = (37.2615t) + (-37.2615t) + -4.9t2 + 4.9t2 Combine like terms: (37.2615t) + (-37.2615t) = 0.0000 -109 + (-37.2615t) + 4.9t2 = 0.0000 + -4.9t2 + 4.9t2 -109 + (-37.2615t) + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -109 + (-37.2615t) + 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'. -22.24489796 + (-7.604387755t) + t2 = 0 Move the constant term to the right: Add '22.24489796' to each side of the equation. -22.24489796 + (-7.604387755t) + 22.24489796 + t2 = 0 + 22.24489796 Reorder the terms: -22.24489796 + 22.24489796 + (-7.604387755t) + t2 = 0 + 22.24489796 Combine like terms: -22.24489796 + 22.24489796 = 0.00000000 0.00000000 + (-7.604387755t) + t2 = 0 + 22.24489796 (-7.604387755t) + t2 = 0 + 22.24489796 Combine like terms: 0 + 22.24489796 = 22.24489796 (-7.604387755t) + t2 = 22.24489796 The t term is (-7.604387755t). Take half its coefficient (-3.802193878). Square it (14.45667829) and add it to both sides. Add '14.45667829' to each side of the equation. (-7.604387755t) + 14.45667829 + t2 = 22.24489796 + 14.45667829 Reorder the terms: 14.45667829 + (-7.604387755t) + t2 = 22.24489796 + 14.45667829 Combine like terms: 22.24489796 + 14.45667829 = 36.70157625 14.45667829 + (-7.604387755t) + t2 = 36.70157625 Factor a perfect square on the left side: (t + -3.802193878)(t + -3.802193878) = 36.70157625 Calculate the square root of the right side: 6.058182586 Break this problem into two subproblems by setting (t + -3.802193878) equal to 6.058182586 and -6.058182586.Subproblem 1
t + -3.802193878 = 6.058182586 Simplifying t + -3.802193878 = 6.058182586 Reorder the terms: -3.802193878 + t = 6.058182586 Solving -3.802193878 + t = 6.058182586 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.802193878' to each side of the equation. -3.802193878 + 3.802193878 + t = 6.058182586 + 3.802193878 Combine like terms: -3.802193878 + 3.802193878 = 0.000000000 0.000000000 + t = 6.058182586 + 3.802193878 t = 6.058182586 + 3.802193878 Combine like terms: 6.058182586 + 3.802193878 = 9.860376464 t = 9.860376464 Simplifying t = 9.860376464Subproblem 2
t + -3.802193878 = -6.058182586 Simplifying t + -3.802193878 = -6.058182586 Reorder the terms: -3.802193878 + t = -6.058182586 Solving -3.802193878 + t = -6.058182586 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.802193878' to each side of the equation. -3.802193878 + 3.802193878 + t = -6.058182586 + 3.802193878 Combine like terms: -3.802193878 + 3.802193878 = 0.000000000 0.000000000 + t = -6.058182586 + 3.802193878 t = -6.058182586 + 3.802193878 Combine like terms: -6.058182586 + 3.802193878 = -2.255988708 t = -2.255988708 Simplifying t = -2.255988708Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.860376464, -2.255988708}
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