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Simplifying 60 = -16t2 + 64t + -60 Reorder the terms: 60 = -60 + 64t + -16t2 Solving 60 = -60 + 64t + -16t2 Solving for variable 't'. Combine like terms: 60 + 60 = 120 120 + -64t + 16t2 = -60 + 64t + -16t2 + 60 + -64t + 16t2 Reorder the terms: 120 + -64t + 16t2 = -60 + 60 + 64t + -64t + -16t2 + 16t2 Combine like terms: -60 + 60 = 0 120 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 120 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 120 + -64t + 16t2 = 0 + -16t2 + 16t2 120 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 120 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(15 + -8t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(15 + -8t + 2t2)' equal to zero and attempt to solve: Simplifying 15 + -8t + 2t2 = 0 Solving 15 + -8t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -4t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -4t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -4t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -4t + t2 = 0 + -7.5 -4t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -4t + t2 = -7.5 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -7.5 + 4 Reorder the terms: 4 + -4t + t2 = -7.5 + 4 Combine like terms: -7.5 + 4 = -3.5 4 + -4t + t2 = -3.5 Factor a perfect square on the left side: (t + -2)(t + -2) = -3.5 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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