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Simplifying -16t2 + 52t = 60 Reorder the terms: 52t + -16t2 = 60 Solving 52t + -16t2 = 60 Solving for variable 't'. Reorder the terms: -60 + 52t + -16t2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 52t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 13t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 13t + -4t2)' equal to zero and attempt to solve: Simplifying -15 + 13t + -4t2 = 0 Solving -15 + 13t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.75 + -3.25t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -3.25t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -3.25t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -3.25t + t2 = 0 + -3.75 -3.25t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -3.25t + t2 = -3.75 The t term is -3.25t. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25t + 2.640625 + t2 = -3.75 + 2.640625 Reorder the terms: 2.640625 + -3.25t + t2 = -3.75 + 2.640625 Combine like terms: -3.75 + 2.640625 = -1.109375 2.640625 + -3.25t + t2 = -1.109375 Factor a perfect square on the left side: (t + -1.625)(t + -1.625) = -1.109375 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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