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Simplifying -16t2 + 48t = 864 Reorder the terms: 48t + -16t2 = 864 Solving 48t + -16t2 = 864 Solving for variable 't'. Reorder the terms: -864 + 48t + -16t2 = 864 + -864 Combine like terms: 864 + -864 = 0 -864 + 48t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-54 + 3t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-54 + 3t + -1t2)' equal to zero and attempt to solve: Simplifying -54 + 3t + -1t2 = 0 Solving -54 + 3t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 54 + -3t + t2 = 0 Move the constant term to the right: Add '-54' to each side of the equation. 54 + -3t + -54 + t2 = 0 + -54 Reorder the terms: 54 + -54 + -3t + t2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -3t + t2 = 0 + -54 -3t + t2 = 0 + -54 Combine like terms: 0 + -54 = -54 -3t + t2 = -54 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = -54 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -54 + 2.25 Combine like terms: -54 + 2.25 = -51.75 2.25 + -3t + t2 = -51.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = -51.75 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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