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Simplifying 120 = -16t2 + 80t Reorder the terms: 120 = 80t + -16t2 Solving 120 = 80t + -16t2 Solving for variable 't'. Reorder the terms: 120 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 120 + -80t + 16t2 = 0 + -16t2 + 16t2 120 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 120 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(15 + -10t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(15 + -10t + 2t2)' equal to zero and attempt to solve: Simplifying 15 + -10t + 2t2 = 0 Solving 15 + -10t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -5t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -5t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -5t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -5t + t2 = 0 + -7.5 -5t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -5t + t2 = -7.5 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -7.5 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -7.5 + 6.25 Combine like terms: -7.5 + 6.25 = -1.25 6.25 + -5t + t2 = -1.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = -1.25 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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