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Simplifying 16t2 + 72t + 88 = 0 Reorder the terms: 88 + 72t + 16t2 = 0 Solving 88 + 72t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(11 + 9t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(11 + 9t + 2t2)' equal to zero and attempt to solve: Simplifying 11 + 9t + 2t2 = 0 Solving 11 + 9t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 4.5t + t2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 4.5t + -5.5 + t2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 4.5t + t2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 4.5t + t2 = 0 + -5.5 4.5t + t2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 4.5t + t2 = -5.5 The t term is 4.5t. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5t + 5.0625 + t2 = -5.5 + 5.0625 Reorder the terms: 5.0625 + 4.5t + t2 = -5.5 + 5.0625 Combine like terms: -5.5 + 5.0625 = -0.4375 5.0625 + 4.5t + t2 = -0.4375 Factor a perfect square on the left side: (t + 2.25)(t + 2.25) = -0.4375 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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