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Simplifying 16t2 + 24t + 16 = 0 Reorder the terms: 16 + 24t + 16t2 = 0 Solving 16 + 24t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(2 + 3t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(2 + 3t + 2t2)' equal to zero and attempt to solve: Simplifying 2 + 3t + 2t2 = 0 Solving 2 + 3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 1.5t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.5t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + 1.5t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5t + t2 = 0 + -1 1.5t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.5t + t2 = -1 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = -1 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + 1.5t + t2 = -0.4375 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = -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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