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Simplifying -16t2 + -3t + -40 = 0 Reorder the terms: -40 + -3t + -16t2 = 0 Solving -40 + -3t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 3t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 3t + 16t2)' equal to zero and attempt to solve: Simplifying 40 + 3t + 16t2 = 0 Solving 40 + 3t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.5 + 0.1875t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 0.1875t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 0.1875t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 0.1875t + t2 = 0 + -2.5 0.1875t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 0.1875t + t2 = -2.5 The t term is 0.1875t. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875t + 0.0087890625 + t2 = -2.5 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875t + t2 = -2.5 + 0.0087890625 Combine like terms: -2.5 + 0.0087890625 = -2.4912109375 0.0087890625 + 0.1875t + t2 = -2.4912109375 Factor a perfect square on the left side: (t + 0.09375)(t + 0.09375) = -2.4912109375 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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