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Simplifying 8t4 + -12t2 + 16 = 0 Reorder the terms: 16 + -12t2 + 8t4 = 0 Solving 16 + -12t2 + 8t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -3t2 + 2t4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -3t2 + 2t4)' equal to zero and attempt to solve: Simplifying 4 + -3t2 + 2t4 = 0 Solving 4 + -3t2 + 2t4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -1.5t2 + t4 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.5t2 + -2 + t4 = 0 + -2 Reorder the terms: 2 + -2 + -1.5t2 + t4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.5t2 + t4 = 0 + -2 -1.5t2 + t4 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.5t2 + t4 = -2 The t term is -1.5t2. 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. -1.5t2 + 0.5625 + t4 = -2 + 0.5625 Reorder the terms: 0.5625 + -1.5t2 + t4 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + -1.5t2 + t4 = -1.4375 Factor a perfect square on the left side: (t2 + -0.75)(t2 + -0.75) = -1.4375 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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