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Simplifying 0 = 16t2 + 12t + 180 Reorder the terms: 0 = 180 + 12t + 16t2 Solving 0 = 180 + 12t + 16t2 Solving for variable 't'. Combine like terms: 0 + -180 = -180 -180 + -12t + -16t2 = 180 + 12t + 16t2 + -180 + -12t + -16t2 Reorder the terms: -180 + -12t + -16t2 = 180 + -180 + 12t + -12t + 16t2 + -16t2 Combine like terms: 180 + -180 = 0 -180 + -12t + -16t2 = 0 + 12t + -12t + 16t2 + -16t2 -180 + -12t + -16t2 = 12t + -12t + 16t2 + -16t2 Combine like terms: 12t + -12t = 0 -180 + -12t + -16t2 = 0 + 16t2 + -16t2 -180 + -12t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -180 + -12t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(45 + 3t + 4t2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(45 + 3t + 4t2)' equal to zero and attempt to solve: Simplifying 45 + 3t + 4t2 = 0 Solving 45 + 3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.25 + 0.75t + t2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + 0.75t + -11.25 + t2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + 0.75t + t2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + 0.75t + t2 = 0 + -11.25 0.75t + t2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 0.75t + t2 = -11.25 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 = -11.25 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = -11.25 + 0.140625 Combine like terms: -11.25 + 0.140625 = -11.109375 0.140625 + 0.75t + t2 = -11.109375 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = -11.109375 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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