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Simplifying 96 = 60t + -16t2 Solving 96 = 60t + -16t2 Solving for variable 't'. Reorder the terms: 96 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 96 + -60t + 16t2 = 0 + -16t2 + 16t2 96 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 96 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(24 + -15t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(24 + -15t + 4t2)' equal to zero and attempt to solve: Simplifying 24 + -15t + 4t2 = 0 Solving 24 + -15t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6 + -3.75t + t2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -3.75t + -6 + t2 = 0 + -6 Reorder the terms: 6 + -6 + -3.75t + t2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -3.75t + t2 = 0 + -6 -3.75t + t2 = 0 + -6 Combine like terms: 0 + -6 = -6 -3.75t + t2 = -6 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = -6 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = -6 + 3.515625 Combine like terms: -6 + 3.515625 = -2.484375 3.515625 + -3.75t + t2 = -2.484375 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = -2.484375 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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