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Simplifying 5.5 = -16t2 + 45t + 0 Reorder the terms: 5.5 = 0 + 45t + -16t2 Remove the zero: 5.5 = 45t + -16t2 Solving 5.5 = 45t + -16t2 Solving for variable 't'. Reorder the terms: 5.5 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 5.5 + -45t + 16t2 = 0 + -16t2 + 16t2 5.5 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 5.5 + -45t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.34375 + -2.8125t + t2 = 0 Move the constant term to the right: Add '-0.34375' to each side of the equation. 0.34375 + -2.8125t + -0.34375 + t2 = 0 + -0.34375 Reorder the terms: 0.34375 + -0.34375 + -2.8125t + t2 = 0 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + -2.8125t + t2 = 0 + -0.34375 -2.8125t + t2 = 0 + -0.34375 Combine like terms: 0 + -0.34375 = -0.34375 -2.8125t + t2 = -0.34375 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = -0.34375 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = -0.34375 + 1.977539063 Combine like terms: -0.34375 + 1.977539063 = 1.633789063 1.977539063 + -2.8125t + t2 = 1.633789063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 1.633789063 Calculate the square root of the right side: 1.278197584 Break this problem into two subproblems by setting (t + -1.40625) equal to 1.278197584 and -1.278197584.Subproblem 1
t + -1.40625 = 1.278197584 Simplifying t + -1.40625 = 1.278197584 Reorder the terms: -1.40625 + t = 1.278197584 Solving -1.40625 + t = 1.278197584 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 1.278197584 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.278197584 + 1.40625 t = 1.278197584 + 1.40625 Combine like terms: 1.278197584 + 1.40625 = 2.684447584 t = 2.684447584 Simplifying t = 2.684447584Subproblem 2
t + -1.40625 = -1.278197584 Simplifying t + -1.40625 = -1.278197584 Reorder the terms: -1.40625 + t = -1.278197584 Solving -1.40625 + t = -1.278197584 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -1.278197584 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.278197584 + 1.40625 t = -1.278197584 + 1.40625 Combine like terms: -1.278197584 + 1.40625 = 0.128052416 t = 0.128052416 Simplifying t = 0.128052416Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.684447584, 0.128052416}
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