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Simplifying -16t2 + 18t = 120 Reorder the terms: 18t + -16t2 = 120 Solving 18t + -16t2 = 120 Solving for variable 't'. Reorder the terms: -120 + 18t + -16t2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 18t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 9t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 9t + -8t2)' equal to zero and attempt to solve: Simplifying -60 + 9t + -8t2 = 0 Solving -60 + 9t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 7.5 + -1.125t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -1.125t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -1.125t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -1.125t + t2 = 0 + -7.5 -1.125t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -1.125t + t2 = -7.5 The t term is -1.125t. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125t + 0.31640625 + t2 = -7.5 + 0.31640625 Reorder the terms: 0.31640625 + -1.125t + t2 = -7.5 + 0.31640625 Combine like terms: -7.5 + 0.31640625 = -7.18359375 0.31640625 + -1.125t + t2 = -7.18359375 Factor a perfect square on the left side: (t + -0.5625)(t + -0.5625) = -7.18359375 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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