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Simplifying 0 = -16t2 + 48t + -52 Reorder the terms: 0 = -52 + 48t + -16t2 Solving 0 = -52 + 48t + -16t2 Solving for variable 't'. Combine like terms: 0 + 52 = 52 52 + -48t + 16t2 = -52 + 48t + -16t2 + 52 + -48t + 16t2 Reorder the terms: 52 + -48t + 16t2 = -52 + 52 + 48t + -48t + -16t2 + 16t2 Combine like terms: -52 + 52 = 0 52 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 52 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 52 + -48t + 16t2 = 0 + -16t2 + 16t2 52 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 52 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(13 + -12t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(13 + -12t + 4t2)' equal to zero and attempt to solve: Simplifying 13 + -12t + 4t2 = 0 Solving 13 + -12t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + -3t + t2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -3t + -3.25 + t2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -3t + t2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -3t + t2 = 0 + -3.25 -3t + t2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -3t + t2 = -3.25 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 = -3.25 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -3.25 + 2.25 Combine like terms: -3.25 + 2.25 = -1 2.25 + -3t + t2 = -1 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = -1 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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