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Simplifying 27.3t + -4.9t2 = 17.5 Solving 27.3t + -4.9t2 = 17.5 Solving for variable 't'. Reorder the terms: -17.5 + 27.3t + -4.9t2 = 17.5 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 -17.5 + 27.3t + -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'. 3.571428571 + -5.571428571t + t2 = 0 Move the constant term to the right: Add '-3.571428571' to each side of the equation. 3.571428571 + -5.571428571t + -3.571428571 + t2 = 0 + -3.571428571 Reorder the terms: 3.571428571 + -3.571428571 + -5.571428571t + t2 = 0 + -3.571428571 Combine like terms: 3.571428571 + -3.571428571 = 0.000000000 0.000000000 + -5.571428571t + t2 = 0 + -3.571428571 -5.571428571t + t2 = 0 + -3.571428571 Combine like terms: 0 + -3.571428571 = -3.571428571 -5.571428571t + t2 = -3.571428571 The t term is -5.571428571t. Take half its coefficient (-2.785714286). Square it (7.760204083) and add it to both sides. Add '7.760204083' to each side of the equation. -5.571428571t + 7.760204083 + t2 = -3.571428571 + 7.760204083 Reorder the terms: 7.760204083 + -5.571428571t + t2 = -3.571428571 + 7.760204083 Combine like terms: -3.571428571 + 7.760204083 = 4.188775512 7.760204083 + -5.571428571t + t2 = 4.188775512 Factor a perfect square on the left side: (t + -2.785714286)(t + -2.785714286) = 4.188775512 Calculate the square root of the right side: 2.046649826 Break this problem into two subproblems by setting (t + -2.785714286) equal to 2.046649826 and -2.046649826.Subproblem 1
t + -2.785714286 = 2.046649826 Simplifying t + -2.785714286 = 2.046649826 Reorder the terms: -2.785714286 + t = 2.046649826 Solving -2.785714286 + t = 2.046649826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.785714286' to each side of the equation. -2.785714286 + 2.785714286 + t = 2.046649826 + 2.785714286 Combine like terms: -2.785714286 + 2.785714286 = 0.000000000 0.000000000 + t = 2.046649826 + 2.785714286 t = 2.046649826 + 2.785714286 Combine like terms: 2.046649826 + 2.785714286 = 4.832364112 t = 4.832364112 Simplifying t = 4.832364112Subproblem 2
t + -2.785714286 = -2.046649826 Simplifying t + -2.785714286 = -2.046649826 Reorder the terms: -2.785714286 + t = -2.046649826 Solving -2.785714286 + t = -2.046649826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.785714286' to each side of the equation. -2.785714286 + 2.785714286 + t = -2.046649826 + 2.785714286 Combine like terms: -2.785714286 + 2.785714286 = 0.000000000 0.000000000 + t = -2.046649826 + 2.785714286 t = -2.046649826 + 2.785714286 Combine like terms: -2.046649826 + 2.785714286 = 0.73906446 t = 0.73906446 Simplifying t = 0.73906446Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.832364112, 0.73906446}
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