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Simplifying -3t2(4t2 + 6t4 + -7) = 0 Reorder the terms: -3t2(-7 + 4t2 + 6t4) = 0 (-7 * -3t2 + 4t2 * -3t2 + 6t4 * -3t2) = 0 (21t2 + -12t4 + -18t6) = 0 Solving 21t2 + -12t4 + -18t6 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t2'. 3t2(7 + -4t2 + -6t4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(7 + -4t2 + -6t4)' equal to zero and attempt to solve: Simplifying 7 + -4t2 + -6t4 = 0 Solving 7 + -4t2 + -6t4 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + 0.6666666667t2 + t4 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 0.6666666667t2 + 1.166666667 + t4 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 0.6666666667t2 + t4 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 0.6666666667t2 + t4 = 0 + 1.166666667 0.6666666667t2 + t4 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 0.6666666667t2 + t4 = 1.166666667 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 = 1.166666667 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667t2 + t4 = 1.166666667 + 0.1111111112 Combine like terms: 1.166666667 + 0.1111111112 = 1.2777777782 0.1111111112 + 0.6666666667t2 + t4 = 1.2777777782 Factor a perfect square on the left side: (t2 + 0.3333333334)(t2 + 0.3333333334) = 1.2777777782 Calculate the square root of the right side: 1.130388331 Break this problem into two subproblems by setting (t2 + 0.3333333334) equal to 1.130388331 and -1.130388331.Subproblem 1
t2 + 0.3333333334 = 1.130388331 Simplifying t2 + 0.3333333334 = 1.130388331 Reorder the terms: 0.3333333334 + t2 = 1.130388331 Solving 0.3333333334 + t2 = 1.130388331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + t2 = 1.130388331 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + t2 = 1.130388331 + -0.3333333334 t2 = 1.130388331 + -0.3333333334 Combine like terms: 1.130388331 + -0.3333333334 = 0.7970549976 t2 = 0.7970549976 Simplifying t2 = 0.7970549976 Take the square root of each side: t = {-0.892779367, 0.892779367}Subproblem 2
t2 + 0.3333333334 = -1.130388331 Simplifying t2 + 0.3333333334 = -1.130388331 Reorder the terms: 0.3333333334 + t2 = -1.130388331 Solving 0.3333333334 + t2 = -1.130388331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + t2 = -1.130388331 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + t2 = -1.130388331 + -0.3333333334 t2 = -1.130388331 + -0.3333333334 Combine like terms: -1.130388331 + -0.3333333334 = -1.4637216644 t2 = -1.4637216644 Simplifying t2 = -1.4637216644 Reorder the terms: 1.4637216644 + t2 = -1.4637216644 + 1.4637216644 Combine like terms: -1.4637216644 + 1.4637216644 = 0.0000000000 1.4637216644 + t2 = 0.0000000000 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. This subproblem is being ignored because a solution could not be determined.Solution
t = {0}
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