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Simplifying 0 = 16t2 + 168t + -50 Reorder the terms: 0 = -50 + 168t + 16t2 Solving 0 = -50 + 168t + 16t2 Solving for variable 't'. Combine like terms: 0 + 50 = 50 50 + -168t + -16t2 = -50 + 168t + 16t2 + 50 + -168t + -16t2 Reorder the terms: 50 + -168t + -16t2 = -50 + 50 + 168t + -168t + 16t2 + -16t2 Combine like terms: -50 + 50 = 0 50 + -168t + -16t2 = 0 + 168t + -168t + 16t2 + -16t2 50 + -168t + -16t2 = 168t + -168t + 16t2 + -16t2 Combine like terms: 168t + -168t = 0 50 + -168t + -16t2 = 0 + 16t2 + -16t2 50 + -168t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 50 + -168t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -84t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -84t + -8t2)' equal to zero and attempt to solve: Simplifying 25 + -84t + -8t2 = 0 Solving 25 + -84t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + 10.5t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 10.5t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 10.5t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 10.5t + t2 = 0 + 3.125 10.5t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 10.5t + t2 = 3.125 The t term is 10.5t. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5t + 27.5625 + t2 = 3.125 + 27.5625 Reorder the terms: 27.5625 + 10.5t + t2 = 3.125 + 27.5625 Combine like terms: 3.125 + 27.5625 = 30.6875 27.5625 + 10.5t + t2 = 30.6875 Factor a perfect square on the left side: (t + 5.25)(t + 5.25) = 30.6875 Calculate the square root of the right side: 5.539629952 Break this problem into two subproblems by setting (t + 5.25) equal to 5.539629952 and -5.539629952.Subproblem 1
t + 5.25 = 5.539629952 Simplifying t + 5.25 = 5.539629952 Reorder the terms: 5.25 + t = 5.539629952 Solving 5.25 + t = 5.539629952 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + t = 5.539629952 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + t = 5.539629952 + -5.25 t = 5.539629952 + -5.25 Combine like terms: 5.539629952 + -5.25 = 0.289629952 t = 0.289629952 Simplifying t = 0.289629952Subproblem 2
t + 5.25 = -5.539629952 Simplifying t + 5.25 = -5.539629952 Reorder the terms: 5.25 + t = -5.539629952 Solving 5.25 + t = -5.539629952 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + t = -5.539629952 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + t = -5.539629952 + -5.25 t = -5.539629952 + -5.25 Combine like terms: -5.539629952 + -5.25 = -10.789629952 t = -10.789629952 Simplifying t = -10.789629952Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.289629952, -10.789629952}Solution
t = {0.289629952, -10.789629952}
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