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Simplifying 10 = -16t2 + -80t + 4 Reorder the terms: 10 = 4 + -80t + -16t2 Solving 10 = 4 + -80t + -16t2 Solving for variable 't'. Combine like terms: 10 + -4 = 6 6 + 80t + 16t2 = 4 + -80t + -16t2 + -4 + 80t + 16t2 Reorder the terms: 6 + 80t + 16t2 = 4 + -4 + -80t + 80t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 6 + 80t + 16t2 = 0 + -80t + 80t + -16t2 + 16t2 6 + 80t + 16t2 = -80t + 80t + -16t2 + 16t2 Combine like terms: -80t + 80t = 0 6 + 80t + 16t2 = 0 + -16t2 + 16t2 6 + 80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 6 + 80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 40t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 40t + 8t2)' equal to zero and attempt to solve: Simplifying 3 + 40t + 8t2 = 0 Solving 3 + 40t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 5t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 5t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 5t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 5t + t2 = 0 + -0.375 5t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 5t + t2 = -0.375 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = -0.375 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -0.375 + 6.25 Combine like terms: -0.375 + 6.25 = 5.875 6.25 + 5t + t2 = 5.875 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 5.875 Calculate the square root of the right side: 2.423839929 Break this problem into two subproblems by setting (t + 2.5) equal to 2.423839929 and -2.423839929.Subproblem 1
t + 2.5 = 2.423839929 Simplifying t + 2.5 = 2.423839929 Reorder the terms: 2.5 + t = 2.423839929 Solving 2.5 + t = 2.423839929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 2.423839929 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 2.423839929 + -2.5 t = 2.423839929 + -2.5 Combine like terms: 2.423839929 + -2.5 = -0.076160071 t = -0.076160071 Simplifying t = -0.076160071Subproblem 2
t + 2.5 = -2.423839929 Simplifying t + 2.5 = -2.423839929 Reorder the terms: 2.5 + t = -2.423839929 Solving 2.5 + t = -2.423839929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -2.423839929 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -2.423839929 + -2.5 t = -2.423839929 + -2.5 Combine like terms: -2.423839929 + -2.5 = -4.923839929 t = -4.923839929 Simplifying t = -4.923839929Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.076160071, -4.923839929}Solution
t = {-0.076160071, -4.923839929}
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