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Simplifying 0 = 3t4 + 2t2 + 8 Reorder the terms: 0 = 8 + 2t2 + 3t4 Solving 0 = 8 + 2t2 + 3t4 Solving for variable 't'. Combine like terms: 0 + -8 = -8 -8 + -2t2 + -3t4 = 8 + 2t2 + 3t4 + -8 + -2t2 + -3t4 Reorder the terms: -8 + -2t2 + -3t4 = 8 + -8 + 2t2 + -2t2 + 3t4 + -3t4 Combine like terms: 8 + -8 = 0 -8 + -2t2 + -3t4 = 0 + 2t2 + -2t2 + 3t4 + -3t4 -8 + -2t2 + -3t4 = 2t2 + -2t2 + 3t4 + -3t4 Combine like terms: 2t2 + -2t2 = 0 -8 + -2t2 + -3t4 = 0 + 3t4 + -3t4 -8 + -2t2 + -3t4 = 3t4 + -3t4 Combine like terms: 3t4 + -3t4 = 0 -8 + -2t2 + -3t4 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 2t2 + 3t4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 2t2 + 3t4)' equal to zero and attempt to solve: Simplifying 8 + 2t2 + 3t4 = 0 Solving 8 + 2t2 + 3t4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 0.6666666667t2 + t4 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 0.6666666667t2 + -2.666666667 + t4 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 0.6666666667t2 + t4 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 0.6666666667t2 + t4 = 0 + -2.666666667 0.6666666667t2 + t4 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 0.6666666667t2 + t4 = -2.666666667 The t term is 0.6666666667t2. 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. 0.6666666667t2 + 0.1111111112 + t4 = -2.666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667t2 + t4 = -2.666666667 + 0.1111111112 Combine like terms: -2.666666667 + 0.1111111112 = -2.5555555558 0.1111111112 + 0.6666666667t2 + t4 = -2.5555555558 Factor a perfect square on the left side: (t2 + 0.3333333334)(t2 + 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. The solution to this equation could not be determined.
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