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Simplifying 48t6 + -27t2 = 0 Reorder the terms: -27t2 + 48t6 = 0 Solving -27t2 + 48t6 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t2'. 3t2(-9 + 16t4) = 0 Factor a difference between two squares. 3t2((3 + 4t2)(-3 + 4t2)) = 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 '(3 + 4t2)' equal to zero and attempt to solve: Simplifying 3 + 4t2 = 0 Solving 3 + 4t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4t2 = 0 + -3 4t2 = 0 + -3 Combine like terms: 0 + -3 = -3 4t2 = -3 Divide each side by '4'. t2 = -0.75 Simplifying t2 = -0.75 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-3 + 4t2)' equal to zero and attempt to solve: Simplifying -3 + 4t2 = 0 Solving -3 + 4t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 4t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4t2 = 0 + 3 4t2 = 0 + 3 Combine like terms: 0 + 3 = 3 4t2 = 3 Divide each side by '4'. t2 = 0.75 Simplifying t2 = 0.75 Take the square root of each side: t = {-0.866025404, 0.866025404}Solution
t = {0, -0.866025404, 0.866025404}
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