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Simplifying 16 = -16t2 + 30t + -4 Reorder the terms: 16 = -4 + 30t + -16t2 Solving 16 = -4 + 30t + -16t2 Solving for variable 't'. Combine like terms: 16 + 4 = 20 20 + -30t + 16t2 = -4 + 30t + -16t2 + 4 + -30t + 16t2 Reorder the terms: 20 + -30t + 16t2 = -4 + 4 + 30t + -30t + -16t2 + 16t2 Combine like terms: -4 + 4 = 0 20 + -30t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2 20 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 20 + -30t + 16t2 = 0 + -16t2 + 16t2 20 + -30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -15t + 8t2)' equal to zero and attempt to solve: Simplifying 10 + -15t + 8t2 = 0 Solving 10 + -15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.25 + -1.875t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -1.875t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -1.875t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -1.875t + t2 = 0 + -1.25 -1.875t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -1.875t + t2 = -1.25 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 = -1.25 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = -1.25 + 0.87890625 Combine like terms: -1.25 + 0.87890625 = -0.37109375 0.87890625 + -1.875t + t2 = -0.37109375 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = -0.37109375 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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