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Simplifying 0 = 8t2 + 71t + 192 Reorder the terms: 0 = 192 + 71t + 8t2 Solving 0 = 192 + 71t + 8t2 Solving for variable 't'. Combine like terms: 0 + -192 = -192 -192 + -71t + -8t2 = 192 + 71t + 8t2 + -192 + -71t + -8t2 Reorder the terms: -192 + -71t + -8t2 = 192 + -192 + 71t + -71t + 8t2 + -8t2 Combine like terms: 192 + -192 = 0 -192 + -71t + -8t2 = 0 + 71t + -71t + 8t2 + -8t2 -192 + -71t + -8t2 = 71t + -71t + 8t2 + -8t2 Combine like terms: 71t + -71t = 0 -192 + -71t + -8t2 = 0 + 8t2 + -8t2 -192 + -71t + -8t2 = 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 -192 + -71t + -8t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(192 + 71t + 8t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(192 + 71t + 8t2)' equal to zero and attempt to solve: Simplifying 192 + 71t + 8t2 = 0 Solving 192 + 71t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 24 + 8.875t + t2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + 8.875t + -24 + t2 = 0 + -24 Reorder the terms: 24 + -24 + 8.875t + t2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 8.875t + t2 = 0 + -24 8.875t + t2 = 0 + -24 Combine like terms: 0 + -24 = -24 8.875t + t2 = -24 The t term is 8.875t. Take half its coefficient (4.4375). Square it (19.69140625) and add it to both sides. Add '19.69140625' to each side of the equation. 8.875t + 19.69140625 + t2 = -24 + 19.69140625 Reorder the terms: 19.69140625 + 8.875t + t2 = -24 + 19.69140625 Combine like terms: -24 + 19.69140625 = -4.30859375 19.69140625 + 8.875t + t2 = -4.30859375 Factor a perfect square on the left side: (t + 4.4375)(t + 4.4375) = -4.30859375 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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