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Simplifying 0 = -16t2 + 96t + -2500 Reorder the terms: 0 = -2500 + 96t + -16t2 Solving 0 = -2500 + 96t + -16t2 Solving for variable 't'. Combine like terms: 0 + 2500 = 2500 2500 + -96t + 16t2 = -2500 + 96t + -16t2 + 2500 + -96t + 16t2 Reorder the terms: 2500 + -96t + 16t2 = -2500 + 2500 + 96t + -96t + -16t2 + 16t2 Combine like terms: -2500 + 2500 = 0 2500 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 2500 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 2500 + -96t + 16t2 = 0 + -16t2 + 16t2 2500 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 2500 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(625 + -24t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(625 + -24t + 4t2)' equal to zero and attempt to solve: Simplifying 625 + -24t + 4t2 = 0 Solving 625 + -24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 156.25 + -6t + t2 = 0 Move the constant term to the right: Add '-156.25' to each side of the equation. 156.25 + -6t + -156.25 + t2 = 0 + -156.25 Reorder the terms: 156.25 + -156.25 + -6t + t2 = 0 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + -6t + t2 = 0 + -156.25 -6t + t2 = 0 + -156.25 Combine like terms: 0 + -156.25 = -156.25 -6t + t2 = -156.25 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 = -156.25 + 9 Reorder the terms: 9 + -6t + t2 = -156.25 + 9 Combine like terms: -156.25 + 9 = -147.25 9 + -6t + t2 = -147.25 Factor a perfect square on the left side: (t + -3)(t + -3) = -147.25 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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