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Simplifying 0 = -16t2 + 55t + 138 Reorder the terms: 0 = 138 + 55t + -16t2 Solving 0 = 138 + 55t + -16t2 Solving for variable 't'. Combine like terms: 0 + -138 = -138 -138 + -55t + 16t2 = 138 + 55t + -16t2 + -138 + -55t + 16t2 Reorder the terms: -138 + -55t + 16t2 = 138 + -138 + 55t + -55t + -16t2 + 16t2 Combine like terms: 138 + -138 = 0 -138 + -55t + 16t2 = 0 + 55t + -55t + -16t2 + 16t2 -138 + -55t + 16t2 = 55t + -55t + -16t2 + 16t2 Combine like terms: 55t + -55t = 0 -138 + -55t + 16t2 = 0 + -16t2 + 16t2 -138 + -55t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -138 + -55t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -8.625 + -3.4375t + t2 = 0 Move the constant term to the right: Add '8.625' to each side of the equation. -8.625 + -3.4375t + 8.625 + t2 = 0 + 8.625 Reorder the terms: -8.625 + 8.625 + -3.4375t + t2 = 0 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + -3.4375t + t2 = 0 + 8.625 -3.4375t + t2 = 0 + 8.625 Combine like terms: 0 + 8.625 = 8.625 -3.4375t + t2 = 8.625 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 = 8.625 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375t + t2 = 8.625 + 2.954101563 Combine like terms: 8.625 + 2.954101563 = 11.579101563 2.954101563 + -3.4375t + t2 = 11.579101563 Factor a perfect square on the left side: (t + -1.71875)(t + -1.71875) = 11.579101563 Calculate the square root of the right side: 3.402807894 Break this problem into two subproblems by setting (t + -1.71875) equal to 3.402807894 and -3.402807894.Subproblem 1
t + -1.71875 = 3.402807894 Simplifying t + -1.71875 = 3.402807894 Reorder the terms: -1.71875 + t = 3.402807894 Solving -1.71875 + t = 3.402807894 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 = 3.402807894 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 3.402807894 + 1.71875 t = 3.402807894 + 1.71875 Combine like terms: 3.402807894 + 1.71875 = 5.121557894 t = 5.121557894 Simplifying t = 5.121557894Subproblem 2
t + -1.71875 = -3.402807894 Simplifying t + -1.71875 = -3.402807894 Reorder the terms: -1.71875 + t = -3.402807894 Solving -1.71875 + t = -3.402807894 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 = -3.402807894 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -3.402807894 + 1.71875 t = -3.402807894 + 1.71875 Combine like terms: -3.402807894 + 1.71875 = -1.684057894 t = -1.684057894 Simplifying t = -1.684057894Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.121557894, -1.684057894}
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