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Simplifying 19.254t2 + -150.696t + 125.28 = 0 Reorder the terms: 125.28 + -150.696t + 19.254t2 = 0 Solving 125.28 + -150.696t + 19.254t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19.254 the coefficient of the squared term: Divide each side by '19.254'. 6.506699907 + -7.826737301t + t2 = 0 Move the constant term to the right: Add '-6.506699907' to each side of the equation. 6.506699907 + -7.826737301t + -6.506699907 + t2 = 0 + -6.506699907 Reorder the terms: 6.506699907 + -6.506699907 + -7.826737301t + t2 = 0 + -6.506699907 Combine like terms: 6.506699907 + -6.506699907 = 0.000000000 0.000000000 + -7.826737301t + t2 = 0 + -6.506699907 -7.826737301t + t2 = 0 + -6.506699907 Combine like terms: 0 + -6.506699907 = -6.506699907 -7.826737301t + t2 = -6.506699907 The t term is -7.826737301t. Take half its coefficient (-3.913368651). Square it (15.31445420) and add it to both sides. Add '15.31445420' to each side of the equation. -7.826737301t + 15.31445420 + t2 = -6.506699907 + 15.31445420 Reorder the terms: 15.31445420 + -7.826737301t + t2 = -6.506699907 + 15.31445420 Combine like terms: -6.506699907 + 15.31445420 = 8.807754293 15.31445420 + -7.826737301t + t2 = 8.807754293 Factor a perfect square on the left side: (t + -3.913368651)(t + -3.913368651) = 8.807754293 Calculate the square root of the right side: 2.967786093 Break this problem into two subproblems by setting (t + -3.913368651) equal to 2.967786093 and -2.967786093.Subproblem 1
t + -3.913368651 = 2.967786093 Simplifying t + -3.913368651 = 2.967786093 Reorder the terms: -3.913368651 + t = 2.967786093 Solving -3.913368651 + t = 2.967786093 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.913368651' to each side of the equation. -3.913368651 + 3.913368651 + t = 2.967786093 + 3.913368651 Combine like terms: -3.913368651 + 3.913368651 = 0.000000000 0.000000000 + t = 2.967786093 + 3.913368651 t = 2.967786093 + 3.913368651 Combine like terms: 2.967786093 + 3.913368651 = 6.881154744 t = 6.881154744 Simplifying t = 6.881154744Subproblem 2
t + -3.913368651 = -2.967786093 Simplifying t + -3.913368651 = -2.967786093 Reorder the terms: -3.913368651 + t = -2.967786093 Solving -3.913368651 + t = -2.967786093 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.913368651' to each side of the equation. -3.913368651 + 3.913368651 + t = -2.967786093 + 3.913368651 Combine like terms: -3.913368651 + 3.913368651 = 0.000000000 0.000000000 + t = -2.967786093 + 3.913368651 t = -2.967786093 + 3.913368651 Combine like terms: -2.967786093 + 3.913368651 = 0.945582558 t = 0.945582558 Simplifying t = 0.945582558Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.881154744, 0.945582558}
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