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Simplifying 0 = -16t2 + 65.5t + 5.5 Reorder the terms: 0 = 5.5 + 65.5t + -16t2 Solving 0 = 5.5 + 65.5t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5.5 = -5.5 -5.5 + -65.5t + 16t2 = 5.5 + 65.5t + -16t2 + -5.5 + -65.5t + 16t2 Reorder the terms: -5.5 + -65.5t + 16t2 = 5.5 + -5.5 + 65.5t + -65.5t + -16t2 + 16t2 Combine like terms: 5.5 + -5.5 = 0.0 -5.5 + -65.5t + 16t2 = 0.0 + 65.5t + -65.5t + -16t2 + 16t2 -5.5 + -65.5t + 16t2 = 65.5t + -65.5t + -16t2 + 16t2 Combine like terms: 65.5t + -65.5t = 0.0 -5.5 + -65.5t + 16t2 = 0.0 + -16t2 + 16t2 -5.5 + -65.5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5.5 + -65.5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.34375 + -4.09375t + t2 = 0 Move the constant term to the right: Add '0.34375' to each side of the equation. -0.34375 + -4.09375t + 0.34375 + t2 = 0 + 0.34375 Reorder the terms: -0.34375 + 0.34375 + -4.09375t + t2 = 0 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + -4.09375t + t2 = 0 + 0.34375 -4.09375t + t2 = 0 + 0.34375 Combine like terms: 0 + 0.34375 = 0.34375 -4.09375t + t2 = 0.34375 The t term is -4.09375t. Take half its coefficient (-2.046875). Square it (4.189697266) and add it to both sides. Add '4.189697266' to each side of the equation. -4.09375t + 4.189697266 + t2 = 0.34375 + 4.189697266 Reorder the terms: 4.189697266 + -4.09375t + t2 = 0.34375 + 4.189697266 Combine like terms: 0.34375 + 4.189697266 = 4.533447266 4.189697266 + -4.09375t + t2 = 4.533447266 Factor a perfect square on the left side: (t + -2.046875)(t + -2.046875) = 4.533447266 Calculate the square root of the right side: 2.129189345 Break this problem into two subproblems by setting (t + -2.046875) equal to 2.129189345 and -2.129189345.Subproblem 1
t + -2.046875 = 2.129189345 Simplifying t + -2.046875 = 2.129189345 Reorder the terms: -2.046875 + t = 2.129189345 Solving -2.046875 + t = 2.129189345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.046875' to each side of the equation. -2.046875 + 2.046875 + t = 2.129189345 + 2.046875 Combine like terms: -2.046875 + 2.046875 = 0.000000 0.000000 + t = 2.129189345 + 2.046875 t = 2.129189345 + 2.046875 Combine like terms: 2.129189345 + 2.046875 = 4.176064345 t = 4.176064345 Simplifying t = 4.176064345Subproblem 2
t + -2.046875 = -2.129189345 Simplifying t + -2.046875 = -2.129189345 Reorder the terms: -2.046875 + t = -2.129189345 Solving -2.046875 + t = -2.129189345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.046875' to each side of the equation. -2.046875 + 2.046875 + t = -2.129189345 + 2.046875 Combine like terms: -2.046875 + 2.046875 = 0.000000 0.000000 + t = -2.129189345 + 2.046875 t = -2.129189345 + 2.046875 Combine like terms: -2.129189345 + 2.046875 = -0.082314345 t = -0.082314345 Simplifying t = -0.082314345Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.176064345, -0.082314345}
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