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Simplifying 6t5 + 4t4 = -2t3 Reorder the terms: 4t4 + 6t5 = -2t3 Solving 4t4 + 6t5 = -2t3 Solving for variable 't'. Reorder the terms: 2t3 + 4t4 + 6t5 = -2t3 + 2t3 Combine like terms: -2t3 + 2t3 = 0 2t3 + 4t4 + 6t5 = 0 Factor out the Greatest Common Factor (GCF), '2t3'. 2t3(1 + 2t + 3t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't3' equal to zero and attempt to solve: Simplifying t3 = 0 Solving t3 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t3 = 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 + 2t + 3t2)' equal to zero and attempt to solve: Simplifying 1 + 2t + 3t2 = 0 Solving 1 + 2t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 0.6666666667t + t2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.6666666667t + -0.3333333333 + t2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.6666666667t + t2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.6666666667t + t2 = 0 + -0.3333333333 0.6666666667t + t2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.6666666667t + t2 = -0.3333333333 The t term is 0.6666666667t. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667t + 0.1111111112 + t2 = -0.3333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667t + t2 = -0.3333333333 + 0.1111111112 Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221 0.1111111112 + 0.6666666667t + t2 = -0.2222222221 Factor a perfect square on the left side: (t + 0.3333333334)(t + 0.3333333334) = -0.2222222221 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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