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Simplifying 0 = 16t2 + 44t + 60 Reorder the terms: 0 = 60 + 44t + 16t2 Solving 0 = 60 + 44t + 16t2 Solving for variable 't'. Combine like terms: 0 + -60 = -60 -60 + -44t + -16t2 = 60 + 44t + 16t2 + -60 + -44t + -16t2 Reorder the terms: -60 + -44t + -16t2 = 60 + -60 + 44t + -44t + 16t2 + -16t2 Combine like terms: 60 + -60 = 0 -60 + -44t + -16t2 = 0 + 44t + -44t + 16t2 + -16t2 -60 + -44t + -16t2 = 44t + -44t + 16t2 + -16t2 Combine like terms: 44t + -44t = 0 -60 + -44t + -16t2 = 0 + 16t2 + -16t2 -60 + -44t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -60 + -44t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(15 + 11t + 4t2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(15 + 11t + 4t2)' equal to zero and attempt to solve: Simplifying 15 + 11t + 4t2 = 0 Solving 15 + 11t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 2.75t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 2.75t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 2.75t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 2.75t + t2 = 0 + -3.75 2.75t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 2.75t + t2 = -3.75 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 = -3.75 + 1.890625 Reorder the terms: 1.890625 + 2.75t + t2 = -3.75 + 1.890625 Combine like terms: -3.75 + 1.890625 = -1.859375 1.890625 + 2.75t + t2 = -1.859375 Factor a perfect square on the left side: (t + 1.375)(t + 1.375) = -1.859375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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