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Simplifying 0 = -16t2 + 30t + 4000 Reorder the terms: 0 = 4000 + 30t + -16t2 Solving 0 = 4000 + 30t + -16t2 Solving for variable 't'. Combine like terms: 0 + -4000 = -4000 -4000 + -30t + 16t2 = 4000 + 30t + -16t2 + -4000 + -30t + 16t2 Reorder the terms: -4000 + -30t + 16t2 = 4000 + -4000 + 30t + -30t + -16t2 + 16t2 Combine like terms: 4000 + -4000 = 0 -4000 + -30t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2 -4000 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 -4000 + -30t + 16t2 = 0 + -16t2 + 16t2 -4000 + -30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4000 + -30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2000 + -15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2000 + -15t + 8t2)' equal to zero and attempt to solve: Simplifying -2000 + -15t + 8t2 = 0 Solving -2000 + -15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -250 + -1.875t + t2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + -1.875t + 250 + t2 = 0 + 250 Reorder the terms: -250 + 250 + -1.875t + t2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -1.875t + t2 = 0 + 250 -1.875t + t2 = 0 + 250 Combine like terms: 0 + 250 = 250 -1.875t + t2 = 250 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 = 250 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = 250 + 0.87890625 Combine like terms: 250 + 0.87890625 = 250.87890625 0.87890625 + -1.875t + t2 = 250.87890625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 250.87890625 Calculate the square root of the right side: 15.839157372 Break this problem into two subproblems by setting (t + -0.9375) equal to 15.839157372 and -15.839157372.Subproblem 1
t + -0.9375 = 15.839157372 Simplifying t + -0.9375 = 15.839157372 Reorder the terms: -0.9375 + t = 15.839157372 Solving -0.9375 + t = 15.839157372 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 = 15.839157372 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 15.839157372 + 0.9375 t = 15.839157372 + 0.9375 Combine like terms: 15.839157372 + 0.9375 = 16.776657372 t = 16.776657372 Simplifying t = 16.776657372Subproblem 2
t + -0.9375 = -15.839157372 Simplifying t + -0.9375 = -15.839157372 Reorder the terms: -0.9375 + t = -15.839157372 Solving -0.9375 + t = -15.839157372 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 = -15.839157372 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -15.839157372 + 0.9375 t = -15.839157372 + 0.9375 Combine like terms: -15.839157372 + 0.9375 = -14.901657372 t = -14.901657372 Simplifying t = -14.901657372Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.776657372, -14.901657372}Solution
t = {16.776657372, -14.901657372}
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