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Simplifying 16t2 + 104t + 560 = 0 Reorder the terms: 560 + 104t + 16t2 = 0 Solving 560 + 104t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(70 + 13t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(70 + 13t + 2t2)' equal to zero and attempt to solve: Simplifying 70 + 13t + 2t2 = 0 Solving 70 + 13t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 35 + 6.5t + t2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + 6.5t + -35 + t2 = 0 + -35 Reorder the terms: 35 + -35 + 6.5t + t2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 6.5t + t2 = 0 + -35 6.5t + t2 = 0 + -35 Combine like terms: 0 + -35 = -35 6.5t + t2 = -35 The t term is 6.5t. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5t + 10.5625 + t2 = -35 + 10.5625 Reorder the terms: 10.5625 + 6.5t + t2 = -35 + 10.5625 Combine like terms: -35 + 10.5625 = -24.4375 10.5625 + 6.5t + t2 = -24.4375 Factor a perfect square on the left side: (t + 3.25)(t + 3.25) = -24.4375 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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