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Simplifying 18t4 + 9t2 + 9 = 0 Reorder the terms: 9 + 9t2 + 18t4 = 0 Solving 9 + 9t2 + 18t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + t2 + 2t4) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + t2 + 2t4)' equal to zero and attempt to solve: Simplifying 1 + t2 + 2t4 = 0 Solving 1 + t2 + 2t4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 0.5t2 + t4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.5t2 + -0.5 + t4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.5t2 + t4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.5t2 + t4 = 0 + -0.5 0.5t2 + t4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.5t2 + t4 = -0.5 The t term is t2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5t2 + 0.25 + t4 = -0.5 + 0.25 Reorder the terms: 0.25 + 0.5t2 + t4 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + 0.5t2 + t4 = -0.25 Factor a perfect square on the left side: (t2 + 0.5)(t2 + 0.5) = -0.25 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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