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Simplifying 420 = -16t2 + 86t + 60 Reorder the terms: 420 = 60 + 86t + -16t2 Solving 420 = 60 + 86t + -16t2 Solving for variable 't'. Combine like terms: 420 + -60 = 360 360 + -86t + 16t2 = 60 + 86t + -16t2 + -60 + -86t + 16t2 Reorder the terms: 360 + -86t + 16t2 = 60 + -60 + 86t + -86t + -16t2 + 16t2 Combine like terms: 60 + -60 = 0 360 + -86t + 16t2 = 0 + 86t + -86t + -16t2 + 16t2 360 + -86t + 16t2 = 86t + -86t + -16t2 + 16t2 Combine like terms: 86t + -86t = 0 360 + -86t + 16t2 = 0 + -16t2 + 16t2 360 + -86t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 360 + -86t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(180 + -43t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(180 + -43t + 8t2)' equal to zero and attempt to solve: Simplifying 180 + -43t + 8t2 = 0 Solving 180 + -43t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 22.5 + -5.375t + t2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -5.375t + -22.5 + t2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -5.375t + t2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -5.375t + t2 = 0 + -22.5 -5.375t + t2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -5.375t + t2 = -22.5 The t term is -5.375t. Take half its coefficient (-2.6875). Square it (7.22265625) and add it to both sides. Add '7.22265625' to each side of the equation. -5.375t + 7.22265625 + t2 = -22.5 + 7.22265625 Reorder the terms: 7.22265625 + -5.375t + t2 = -22.5 + 7.22265625 Combine like terms: -22.5 + 7.22265625 = -15.27734375 7.22265625 + -5.375t + t2 = -15.27734375 Factor a perfect square on the left side: (t + -2.6875)(t + -2.6875) = -15.27734375 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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