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Simplifying 11t2 + 9t3 + -5t3 + -5t2 + -3t2 + -7t4 = 0 Reorder the terms: 11t2 + -5t2 + -3t2 + 9t3 + -5t3 + -7t4 = 0 Combine like terms: 11t2 + -5t2 = 6t2 6t2 + -3t2 + 9t3 + -5t3 + -7t4 = 0 Combine like terms: 6t2 + -3t2 = 3t2 3t2 + 9t3 + -5t3 + -7t4 = 0 Combine like terms: 9t3 + -5t3 = 4t3 3t2 + 4t3 + -7t4 = 0 Solving 3t2 + 4t3 + -7t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(3 + 4t + -7t2) = 0 Factor a trinomial. t2((1 + -1t)(3 + 7t)) = 0Subproblem 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 '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 3
Set the factor '(3 + 7t)' equal to zero and attempt to solve: Simplifying 3 + 7t = 0 Solving 3 + 7t = 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 + 7t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7t = 0 + -3 7t = 0 + -3 Combine like terms: 0 + -3 = -3 7t = -3 Divide each side by '7'. t = -0.4285714286 Simplifying t = -0.4285714286Solution
t = {0, 1, -0.4285714286}
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