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Simplifying 0 = -16t2 + -55t + 10 Reorder the terms: 0 = 10 + -55t + -16t2 Solving 0 = 10 + -55t + -16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + 55t + 16t2 = 10 + -55t + -16t2 + -10 + 55t + 16t2 Reorder the terms: -10 + 55t + 16t2 = 10 + -10 + -55t + 55t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + 55t + 16t2 = 0 + -55t + 55t + -16t2 + 16t2 -10 + 55t + 16t2 = -55t + 55t + -16t2 + 16t2 Combine like terms: -55t + 55t = 0 -10 + 55t + 16t2 = 0 + -16t2 + 16t2 -10 + 55t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + 55t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.625 + 3.4375t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 3.4375t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 3.4375t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 3.4375t + t2 = 0 + 0.625 3.4375t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 3.4375t + t2 = 0.625 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 = 0.625 + 2.954101563 Reorder the terms: 2.954101563 + 3.4375t + t2 = 0.625 + 2.954101563 Combine like terms: 0.625 + 2.954101563 = 3.579101563 2.954101563 + 3.4375t + t2 = 3.579101563 Factor a perfect square on the left side: (t + 1.71875)(t + 1.71875) = 3.579101563 Calculate the square root of the right side: 1.891851359 Break this problem into two subproblems by setting (t + 1.71875) equal to 1.891851359 and -1.891851359.Subproblem 1
t + 1.71875 = 1.891851359 Simplifying t + 1.71875 = 1.891851359 Reorder the terms: 1.71875 + t = 1.891851359 Solving 1.71875 + t = 1.891851359 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 = 1.891851359 + -1.71875 Combine like terms: 1.71875 + -1.71875 = 0.00000 0.00000 + t = 1.891851359 + -1.71875 t = 1.891851359 + -1.71875 Combine like terms: 1.891851359 + -1.71875 = 0.173101359 t = 0.173101359 Simplifying t = 0.173101359Subproblem 2
t + 1.71875 = -1.891851359 Simplifying t + 1.71875 = -1.891851359 Reorder the terms: 1.71875 + t = -1.891851359 Solving 1.71875 + t = -1.891851359 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 = -1.891851359 + -1.71875 Combine like terms: 1.71875 + -1.71875 = 0.00000 0.00000 + t = -1.891851359 + -1.71875 t = -1.891851359 + -1.71875 Combine like terms: -1.891851359 + -1.71875 = -3.610601359 t = -3.610601359 Simplifying t = -3.610601359Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.173101359, -3.610601359}
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