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Simplifying 0 = 16t2 + -4t + 2 Reorder the terms: 0 = 2 + -4t + 16t2 Solving 0 = 2 + -4t + 16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + 4t + -16t2 = 2 + -4t + 16t2 + -2 + 4t + -16t2 Reorder the terms: -2 + 4t + -16t2 = 2 + -2 + -4t + 4t + 16t2 + -16t2 Combine like terms: 2 + -2 = 0 -2 + 4t + -16t2 = 0 + -4t + 4t + 16t2 + -16t2 -2 + 4t + -16t2 = -4t + 4t + 16t2 + -16t2 Combine like terms: -4t + 4t = 0 -2 + 4t + -16t2 = 0 + 16t2 + -16t2 -2 + 4t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -2 + 4t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2t + -8t2)' equal to zero and attempt to solve: Simplifying -1 + 2t + -8t2 = 0 Solving -1 + 2t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.125 + -0.25t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.25t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.25t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.25t + t2 = 0 + -0.125 -0.25t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -0.25t + t2 = -0.125 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = -0.125 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = -0.125 + 0.015625 Combine like terms: -0.125 + 0.015625 = -0.109375 0.015625 + -0.25t + t2 = -0.109375 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = -0.109375 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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