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Simplifying 0 = 16t2 + -8t + 12 Reorder the terms: 0 = 12 + -8t + 16t2 Solving 0 = 12 + -8t + 16t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + 8t + -16t2 = 12 + -8t + 16t2 + -12 + 8t + -16t2 Reorder the terms: -12 + 8t + -16t2 = 12 + -12 + -8t + 8t + 16t2 + -16t2 Combine like terms: 12 + -12 = 0 -12 + 8t + -16t2 = 0 + -8t + 8t + 16t2 + -16t2 -12 + 8t + -16t2 = -8t + 8t + 16t2 + -16t2 Combine like terms: -8t + 8t = 0 -12 + 8t + -16t2 = 0 + 16t2 + -16t2 -12 + 8t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -12 + 8t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 2t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 2t + -4t2)' equal to zero and attempt to solve: Simplifying -3 + 2t + -4t2 = 0 Solving -3 + 2t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.75 + -0.5t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.5t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.5t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.5t + t2 = 0 + -0.75 -0.5t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.5t + t2 = -0.75 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = -0.75 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + -0.5t + t2 = -0.6875 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = -0.6875 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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