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Simplifying 18t5 + -12t4 + 6t3 = 0 Reorder the terms: 6t3 + -12t4 + 18t5 = 0 Solving 6t3 + -12t4 + 18t5 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '6t3'. 6t3(1 + -2t + 3t2) = 0 Ignore the factor 6.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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