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Simplifying 200 = -16t2 + 96t Reorder the terms: 200 = 96t + -16t2 Solving 200 = 96t + -16t2 Solving for variable 't'. Reorder the terms: 200 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 200 + -96t + 16t2 = 0 + -16t2 + 16t2 200 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 200 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(25 + -12t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + -12t + 2t2)' equal to zero and attempt to solve: Simplifying 25 + -12t + 2t2 = 0 Solving 25 + -12t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -6t + t2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -6t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -6t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -6t + t2 = 0 + -12.5 -6t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -6t + t2 = -12.5 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -12.5 + 9 Reorder the terms: 9 + -6t + t2 = -12.5 + 9 Combine like terms: -12.5 + 9 = -3.5 9 + -6t + t2 = -3.5 Factor a perfect square on the left side: (t + -3)(t + -3) = -3.5 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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