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Simplifying 16t2 + 18t + 24 = 0 Reorder the terms: 24 + 18t + 16t2 = 0 Solving 24 + 18t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 9t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 9t + 8t2)' equal to zero and attempt to solve: Simplifying 12 + 9t + 8t2 = 0 Solving 12 + 9t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + 1.125t + t2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.125t + -1.5 + t2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.125t + t2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.125t + t2 = 0 + -1.5 1.125t + t2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.125t + t2 = -1.5 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 = -1.5 + 0.31640625 Reorder the terms: 0.31640625 + 1.125t + t2 = -1.5 + 0.31640625 Combine like terms: -1.5 + 0.31640625 = -1.18359375 0.31640625 + 1.125t + t2 = -1.18359375 Factor a perfect square on the left side: (t + 0.5625)(t + 0.5625) = -1.18359375 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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