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Simplifying 0 = -16t2 + 30t + -44 Reorder the terms: 0 = -44 + 30t + -16t2 Solving 0 = -44 + 30t + -16t2 Solving for variable 't'. Combine like terms: 0 + 44 = 44 44 + -30t + 16t2 = -44 + 30t + -16t2 + 44 + -30t + 16t2 Reorder the terms: 44 + -30t + 16t2 = -44 + 44 + 30t + -30t + -16t2 + 16t2 Combine like terms: -44 + 44 = 0 44 + -30t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2 44 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 44 + -30t + 16t2 = 0 + -16t2 + 16t2 44 + -30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 44 + -30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(22 + -15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(22 + -15t + 8t2)' equal to zero and attempt to solve: Simplifying 22 + -15t + 8t2 = 0 Solving 22 + -15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.75 + -1.875t + t2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -1.875t + -2.75 + t2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -1.875t + t2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -1.875t + t2 = 0 + -2.75 -1.875t + t2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -1.875t + t2 = -2.75 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 = -2.75 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = -2.75 + 0.87890625 Combine like terms: -2.75 + 0.87890625 = -1.87109375 0.87890625 + -1.875t + t2 = -1.87109375 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = -1.87109375 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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