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Simplifying 3t3 + -2t2 + 8t = 0 Reorder the terms: 8t + -2t2 + 3t3 = 0 Solving 8t + -2t2 + 3t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(8 + -2t + 3t2) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(8 + -2t + 3t2)' equal to zero and attempt to solve: Simplifying 8 + -2t + 3t2 = 0 Solving 8 + -2t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + -0.6666666667t + t2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -0.6666666667t + -2.666666667 + t2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -0.6666666667t + t2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -0.6666666667t + t2 = 0 + -2.666666667 -0.6666666667t + t2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -0.6666666667t + t2 = -2.666666667 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 = -2.666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667t + t2 = -2.666666667 + 0.1111111112 Combine like terms: -2.666666667 + 0.1111111112 = -2.5555555558 0.1111111112 + -0.6666666667t + t2 = -2.5555555558 Factor a perfect square on the left side: (t + -0.3333333334)(t + -0.3333333334) = -2.5555555558 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.Solution
t = {0}
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