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Simplifying 2t3(t + -1t2 + 3t3) = 0 (t * 2t3 + -1t2 * 2t3 + 3t3 * 2t3) = 0 (2t4 + -2t5 + 6t6) = 0 Solving 2t4 + -2t5 + 6t6 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t4'. 2t4(1 + -1t + 3t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't4' equal to zero and attempt to solve: Simplifying t4 = 0 Solving t4 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -1t + 3t2)' equal to zero and attempt to solve: Simplifying 1 + -1t + 3t2 = 0 Solving 1 + -1t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -0.3333333333t + t2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.3333333333t + -0.3333333333 + t2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.3333333333t + t2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.3333333333t + t2 = 0 + -0.3333333333 -0.3333333333t + t2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.3333333333t + t2 = -0.3333333333 The t term is -0.3333333333t. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333t + 0.02777777779 + t2 = -0.3333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333t + t2 = -0.3333333333 + 0.02777777779 Combine like terms: -0.3333333333 + 0.02777777779 = -0.30555555551 0.02777777779 + -0.3333333333t + t2 = -0.30555555551 Factor a perfect square on the left side: (t + -0.1666666667)(t + -0.1666666667) = -0.30555555551 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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