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Simplifying 0 = -16t2 + -30t + 600 Reorder the terms: 0 = 600 + -30t + -16t2 Solving 0 = 600 + -30t + -16t2 Solving for variable 't'. Combine like terms: 0 + -600 = -600 -600 + 30t + 16t2 = 600 + -30t + -16t2 + -600 + 30t + 16t2 Reorder the terms: -600 + 30t + 16t2 = 600 + -600 + -30t + 30t + -16t2 + 16t2 Combine like terms: 600 + -600 = 0 -600 + 30t + 16t2 = 0 + -30t + 30t + -16t2 + 16t2 -600 + 30t + 16t2 = -30t + 30t + -16t2 + 16t2 Combine like terms: -30t + 30t = 0 -600 + 30t + 16t2 = 0 + -16t2 + 16t2 -600 + 30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -600 + 30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-300 + 15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-300 + 15t + 8t2)' equal to zero and attempt to solve: Simplifying -300 + 15t + 8t2 = 0 Solving -300 + 15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -37.5 + 1.875t + t2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 1.875t + 37.5 + t2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 1.875t + t2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 1.875t + t2 = 0 + 37.5 1.875t + t2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 1.875t + t2 = 37.5 The t term is 1.875t. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875t + 0.87890625 + t2 = 37.5 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 37.5 + 0.87890625 Combine like terms: 37.5 + 0.87890625 = 38.37890625 0.87890625 + 1.875t + t2 = 38.37890625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 38.37890625 Calculate the square root of the right side: 6.195071126 Break this problem into two subproblems by setting (t + 0.9375) equal to 6.195071126 and -6.195071126.Subproblem 1
t + 0.9375 = 6.195071126 Simplifying t + 0.9375 = 6.195071126 Reorder the terms: 0.9375 + t = 6.195071126 Solving 0.9375 + t = 6.195071126 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = 6.195071126 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 6.195071126 + -0.9375 t = 6.195071126 + -0.9375 Combine like terms: 6.195071126 + -0.9375 = 5.257571126 t = 5.257571126 Simplifying t = 5.257571126Subproblem 2
t + 0.9375 = -6.195071126 Simplifying t + 0.9375 = -6.195071126 Reorder the terms: 0.9375 + t = -6.195071126 Solving 0.9375 + t = -6.195071126 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = -6.195071126 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -6.195071126 + -0.9375 t = -6.195071126 + -0.9375 Combine like terms: -6.195071126 + -0.9375 = -7.132571126 t = -7.132571126 Simplifying t = -7.132571126Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.257571126, -7.132571126}Solution
t = {5.257571126, -7.132571126}
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