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Simplifying -16t2 + -16t + -840 = 0 Reorder the terms: -840 + -16t + -16t2 = 0 Solving -840 + -16t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-8'. -8(105 + 2t + 2t2) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(105 + 2t + 2t2)' equal to zero and attempt to solve: Simplifying 105 + 2t + 2t2 = 0 Solving 105 + 2t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 52.5 + t + t2 = 0 Move the constant term to the right: Add '-52.5' to each side of the equation. 52.5 + t + -52.5 + t2 = 0 + -52.5 Reorder the terms: 52.5 + -52.5 + t + t2 = 0 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + t + t2 = 0 + -52.5 t + t2 = 0 + -52.5 Combine like terms: 0 + -52.5 = -52.5 t + t2 = -52.5 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = -52.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = -52.5 + 0.25 Combine like terms: -52.5 + 0.25 = -52.25 1.25 + t2 = -52.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -52.25 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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