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Simplifying 0 = -16t2 + 150t + 155 Reorder the terms: 0 = 155 + 150t + -16t2 Solving 0 = 155 + 150t + -16t2 Solving for variable 't'. Combine like terms: 0 + -155 = -155 -155 + -150t + 16t2 = 155 + 150t + -16t2 + -155 + -150t + 16t2 Reorder the terms: -155 + -150t + 16t2 = 155 + -155 + 150t + -150t + -16t2 + 16t2 Combine like terms: 155 + -155 = 0 -155 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -155 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -155 + -150t + 16t2 = 0 + -16t2 + 16t2 -155 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -155 + -150t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9.6875 + -9.375t + t2 = 0 Move the constant term to the right: Add '9.6875' to each side of the equation. -9.6875 + -9.375t + 9.6875 + t2 = 0 + 9.6875 Reorder the terms: -9.6875 + 9.6875 + -9.375t + t2 = 0 + 9.6875 Combine like terms: -9.6875 + 9.6875 = 0.0000 0.0000 + -9.375t + t2 = 0 + 9.6875 -9.375t + t2 = 0 + 9.6875 Combine like terms: 0 + 9.6875 = 9.6875 -9.375t + t2 = 9.6875 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = 9.6875 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 9.6875 + 21.97265625 Combine like terms: 9.6875 + 21.97265625 = 31.66015625 21.97265625 + -9.375t + t2 = 31.66015625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 31.66015625 Calculate the square root of the right side: 5.626735843 Break this problem into two subproblems by setting (t + -4.6875) equal to 5.626735843 and -5.626735843.Subproblem 1
t + -4.6875 = 5.626735843 Simplifying t + -4.6875 = 5.626735843 Reorder the terms: -4.6875 + t = 5.626735843 Solving -4.6875 + t = 5.626735843 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 5.626735843 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 5.626735843 + 4.6875 t = 5.626735843 + 4.6875 Combine like terms: 5.626735843 + 4.6875 = 10.314235843 t = 10.314235843 Simplifying t = 10.314235843Subproblem 2
t + -4.6875 = -5.626735843 Simplifying t + -4.6875 = -5.626735843 Reorder the terms: -4.6875 + t = -5.626735843 Solving -4.6875 + t = -5.626735843 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -5.626735843 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -5.626735843 + 4.6875 t = -5.626735843 + 4.6875 Combine like terms: -5.626735843 + 4.6875 = -0.939235843 t = -0.939235843 Simplifying t = -0.939235843Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.314235843, -0.939235843}
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