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Simplifying 0 = -16t2 + 160t + 6 Reorder the terms: 0 = 6 + 160t + -16t2 Solving 0 = 6 + 160t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -160t + 16t2 = 6 + 160t + -16t2 + -6 + -160t + 16t2 Reorder the terms: -6 + -160t + 16t2 = 6 + -6 + 160t + -160t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2 -6 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 -6 + -160t + 16t2 = 0 + -16t2 + 16t2 -6 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -80t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -80t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + -80t + 8t2 = 0 Solving -3 + -80t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -10t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -10t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -10t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -10t + t2 = 0 + 0.375 -10t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -10t + t2 = 0.375 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 0.375 + 25 Reorder the terms: 25 + -10t + t2 = 0.375 + 25 Combine like terms: 0.375 + 25 = 25.375 25 + -10t + t2 = 25.375 Factor a perfect square on the left side: (t + -5)(t + -5) = 25.375 Calculate the square root of the right side: 5.03736042 Break this problem into two subproblems by setting (t + -5) equal to 5.03736042 and -5.03736042.Subproblem 1
t + -5 = 5.03736042 Simplifying t + -5 = 5.03736042 Reorder the terms: -5 + t = 5.03736042 Solving -5 + t = 5.03736042 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.03736042 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.03736042 + 5 t = 5.03736042 + 5 Combine like terms: 5.03736042 + 5 = 10.03736042 t = 10.03736042 Simplifying t = 10.03736042Subproblem 2
t + -5 = -5.03736042 Simplifying t + -5 = -5.03736042 Reorder the terms: -5 + t = -5.03736042 Solving -5 + t = -5.03736042 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.03736042 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.03736042 + 5 t = -5.03736042 + 5 Combine like terms: -5.03736042 + 5 = -0.03736042 t = -0.03736042 Simplifying t = -0.03736042Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.03736042, -0.03736042}Solution
t = {10.03736042, -0.03736042}
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