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Simplifying 0 = -16t2 + 146t + -20 Reorder the terms: 0 = -20 + 146t + -16t2 Solving 0 = -20 + 146t + -16t2 Solving for variable 't'. Combine like terms: 0 + 20 = 20 20 + -146t + 16t2 = -20 + 146t + -16t2 + 20 + -146t + 16t2 Reorder the terms: 20 + -146t + 16t2 = -20 + 20 + 146t + -146t + -16t2 + 16t2 Combine like terms: -20 + 20 = 0 20 + -146t + 16t2 = 0 + 146t + -146t + -16t2 + 16t2 20 + -146t + 16t2 = 146t + -146t + -16t2 + 16t2 Combine like terms: 146t + -146t = 0 20 + -146t + 16t2 = 0 + -16t2 + 16t2 20 + -146t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -146t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -73t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -73t + 8t2)' equal to zero and attempt to solve: Simplifying 10 + -73t + 8t2 = 0 Solving 10 + -73t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.25 + -9.125t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -9.125t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -9.125t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -9.125t + t2 = 0 + -1.25 -9.125t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -9.125t + t2 = -1.25 The t term is -9.125t. Take half its coefficient (-4.5625). Square it (20.81640625) and add it to both sides. Add '20.81640625' to each side of the equation. -9.125t + 20.81640625 + t2 = -1.25 + 20.81640625 Reorder the terms: 20.81640625 + -9.125t + t2 = -1.25 + 20.81640625 Combine like terms: -1.25 + 20.81640625 = 19.56640625 20.81640625 + -9.125t + t2 = 19.56640625 Factor a perfect square on the left side: (t + -4.5625)(t + -4.5625) = 19.56640625 Calculate the square root of the right side: 4.42339307 Break this problem into two subproblems by setting (t + -4.5625) equal to 4.42339307 and -4.42339307.Subproblem 1
t + -4.5625 = 4.42339307 Simplifying t + -4.5625 = 4.42339307 Reorder the terms: -4.5625 + t = 4.42339307 Solving -4.5625 + t = 4.42339307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5625' to each side of the equation. -4.5625 + 4.5625 + t = 4.42339307 + 4.5625 Combine like terms: -4.5625 + 4.5625 = 0.0000 0.0000 + t = 4.42339307 + 4.5625 t = 4.42339307 + 4.5625 Combine like terms: 4.42339307 + 4.5625 = 8.98589307 t = 8.98589307 Simplifying t = 8.98589307Subproblem 2
t + -4.5625 = -4.42339307 Simplifying t + -4.5625 = -4.42339307 Reorder the terms: -4.5625 + t = -4.42339307 Solving -4.5625 + t = -4.42339307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5625' to each side of the equation. -4.5625 + 4.5625 + t = -4.42339307 + 4.5625 Combine like terms: -4.5625 + 4.5625 = 0.0000 0.0000 + t = -4.42339307 + 4.5625 t = -4.42339307 + 4.5625 Combine like terms: -4.42339307 + 4.5625 = 0.13910693 t = 0.13910693 Simplifying t = 0.13910693Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.98589307, 0.13910693}Solution
t = {8.98589307, 0.13910693}
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