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Simplifying 30 = -16t2 + 55t Reorder the terms: 30 = 55t + -16t2 Solving 30 = 55t + -16t2 Solving for variable 't'. Reorder the terms: 30 + -55t + 16t2 = 55t + -55t + -16t2 + 16t2 Combine like terms: 55t + -55t = 0 30 + -55t + 16t2 = 0 + -16t2 + 16t2 30 + -55t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 30 + -55t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.875 + -3.4375t + t2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -3.4375t + -1.875 + t2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -3.4375t + t2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -3.4375t + t2 = 0 + -1.875 -3.4375t + t2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -3.4375t + t2 = -1.875 The t term is -3.4375t. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375t + 2.954101563 + t2 = -1.875 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375t + t2 = -1.875 + 2.954101563 Combine like terms: -1.875 + 2.954101563 = 1.079101563 2.954101563 + -3.4375t + t2 = 1.079101563 Factor a perfect square on the left side: (t + -1.71875)(t + -1.71875) = 1.079101563 Calculate the square root of the right side: 1.038798134 Break this problem into two subproblems by setting (t + -1.71875) equal to 1.038798134 and -1.038798134.Subproblem 1
t + -1.71875 = 1.038798134 Simplifying t + -1.71875 = 1.038798134 Reorder the terms: -1.71875 + t = 1.038798134 Solving -1.71875 + t = 1.038798134 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = 1.038798134 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 1.038798134 + 1.71875 t = 1.038798134 + 1.71875 Combine like terms: 1.038798134 + 1.71875 = 2.757548134 t = 2.757548134 Simplifying t = 2.757548134Subproblem 2
t + -1.71875 = -1.038798134 Simplifying t + -1.71875 = -1.038798134 Reorder the terms: -1.71875 + t = -1.038798134 Solving -1.71875 + t = -1.038798134 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = -1.038798134 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -1.038798134 + 1.71875 t = -1.038798134 + 1.71875 Combine like terms: -1.038798134 + 1.71875 = 0.679951866 t = 0.679951866 Simplifying t = 0.679951866Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.757548134, 0.679951866}
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