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Simplifying -16t2 + 96t = 288 Reorder the terms: 96t + -16t2 = 288 Solving 96t + -16t2 = 288 Solving for variable 't'. Reorder the terms: -288 + 96t + -16t2 = 288 + -288 Combine like terms: 288 + -288 = 0 -288 + 96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-18 + 6t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-18 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying -18 + 6t + -1t2 = 0 Solving -18 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -6t + t2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -6t + -18 + t2 = 0 + -18 Reorder the terms: 18 + -18 + -6t + t2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -6t + t2 = 0 + -18 -6t + t2 = 0 + -18 Combine like terms: 0 + -18 = -18 -6t + t2 = -18 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 = -18 + 9 Reorder the terms: 9 + -6t + t2 = -18 + 9 Combine like terms: -18 + 9 = -9 9 + -6t + t2 = -9 Factor a perfect square on the left side: (t + -3)(t + -3) = -9 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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