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Simplifying 16t2 + 12t + 432 = 0 Reorder the terms: 432 + 12t + 16t2 = 0 Solving 432 + 12t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(108 + 3t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(108 + 3t + 4t2)' equal to zero and attempt to solve: Simplifying 108 + 3t + 4t2 = 0 Solving 108 + 3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 27 + 0.75t + t2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 0.75t + -27 + t2 = 0 + -27 Reorder the terms: 27 + -27 + 0.75t + t2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 0.75t + t2 = 0 + -27 0.75t + t2 = 0 + -27 Combine like terms: 0 + -27 = -27 0.75t + t2 = -27 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = -27 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = -27 + 0.140625 Combine like terms: -27 + 0.140625 = -26.859375 0.140625 + 0.75t + t2 = -26.859375 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = -26.859375 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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