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Simplifying 0 = -16t2 + 44t + 320 Reorder the terms: 0 = 320 + 44t + -16t2 Solving 0 = 320 + 44t + -16t2 Solving for variable 't'. Combine like terms: 0 + -320 = -320 -320 + -44t + 16t2 = 320 + 44t + -16t2 + -320 + -44t + 16t2 Reorder the terms: -320 + -44t + 16t2 = 320 + -320 + 44t + -44t + -16t2 + 16t2 Combine like terms: 320 + -320 = 0 -320 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2 -320 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2 Combine like terms: 44t + -44t = 0 -320 + -44t + 16t2 = 0 + -16t2 + 16t2 -320 + -44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -320 + -44t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-80 + -11t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-80 + -11t + 4t2)' equal to zero and attempt to solve: Simplifying -80 + -11t + 4t2 = 0 Solving -80 + -11t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -20 + -2.75t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -2.75t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -2.75t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2.75t + t2 = 0 + 20 -2.75t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2.75t + t2 = 20 The t term is -2.75t. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75t + 1.890625 + t2 = 20 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = 20 + 1.890625 Combine like terms: 20 + 1.890625 = 21.890625 1.890625 + -2.75t + t2 = 21.890625 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = 21.890625 Calculate the square root of the right side: 4.678741818 Break this problem into two subproblems by setting (t + -1.375) equal to 4.678741818 and -4.678741818.Subproblem 1
t + -1.375 = 4.678741818 Simplifying t + -1.375 = 4.678741818 Reorder the terms: -1.375 + t = 4.678741818 Solving -1.375 + t = 4.678741818 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = 4.678741818 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = 4.678741818 + 1.375 t = 4.678741818 + 1.375 Combine like terms: 4.678741818 + 1.375 = 6.053741818 t = 6.053741818 Simplifying t = 6.053741818Subproblem 2
t + -1.375 = -4.678741818 Simplifying t + -1.375 = -4.678741818 Reorder the terms: -1.375 + t = -4.678741818 Solving -1.375 + t = -4.678741818 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = -4.678741818 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = -4.678741818 + 1.375 t = -4.678741818 + 1.375 Combine like terms: -4.678741818 + 1.375 = -3.303741818 t = -3.303741818 Simplifying t = -3.303741818Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.053741818, -3.303741818}Solution
t = {6.053741818, -3.303741818}
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