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Simplifying 16t2 + 30t + 78 = 0 Reorder the terms: 78 + 30t + 16t2 = 0 Solving 78 + 30t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(39 + 15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(39 + 15t + 8t2)' equal to zero and attempt to solve: Simplifying 39 + 15t + 8t2 = 0 Solving 39 + 15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 4.875 + 1.875t + t2 = 0 Move the constant term to the right: Add '-4.875' to each side of the equation. 4.875 + 1.875t + -4.875 + t2 = 0 + -4.875 Reorder the terms: 4.875 + -4.875 + 1.875t + t2 = 0 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + 1.875t + t2 = 0 + -4.875 1.875t + t2 = 0 + -4.875 Combine like terms: 0 + -4.875 = -4.875 1.875t + t2 = -4.875 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 = -4.875 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = -4.875 + 0.87890625 Combine like terms: -4.875 + 0.87890625 = -3.99609375 0.87890625 + 1.875t + t2 = -3.99609375 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = -3.99609375 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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