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Simplifying 300 = -16t2 + 120t + 4 Reorder the terms: 300 = 4 + 120t + -16t2 Solving 300 = 4 + 120t + -16t2 Solving for variable 't'. Combine like terms: 300 + -4 = 296 296 + -120t + 16t2 = 4 + 120t + -16t2 + -4 + -120t + 16t2 Reorder the terms: 296 + -120t + 16t2 = 4 + -4 + 120t + -120t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 296 + -120t + 16t2 = 0 + 120t + -120t + -16t2 + 16t2 296 + -120t + 16t2 = 120t + -120t + -16t2 + 16t2 Combine like terms: 120t + -120t = 0 296 + -120t + 16t2 = 0 + -16t2 + 16t2 296 + -120t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 296 + -120t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(37 + -15t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(37 + -15t + 2t2)' equal to zero and attempt to solve: Simplifying 37 + -15t + 2t2 = 0 Solving 37 + -15t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18.5 + -7.5t + t2 = 0 Move the constant term to the right: Add '-18.5' to each side of the equation. 18.5 + -7.5t + -18.5 + t2 = 0 + -18.5 Reorder the terms: 18.5 + -18.5 + -7.5t + t2 = 0 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -7.5t + t2 = 0 + -18.5 -7.5t + t2 = 0 + -18.5 Combine like terms: 0 + -18.5 = -18.5 -7.5t + t2 = -18.5 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = -18.5 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = -18.5 + 14.0625 Combine like terms: -18.5 + 14.0625 = -4.4375 14.0625 + -7.5t + t2 = -4.4375 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = -4.4375 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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