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Simplifying 324t2 + 144t + 16 = 0 Reorder the terms: 16 + 144t + 324t2 = 0 Solving 16 + 144t + 324t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 36t + 81t2) = 0 Factor a trinomial. 4((2 + 9t)(2 + 9t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + 9t)' equal to zero and attempt to solve: Simplifying 2 + 9t = 0 Solving 2 + 9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9t = 0 + -2 9t = 0 + -2 Combine like terms: 0 + -2 = -2 9t = -2 Divide each side by '9'. t = -0.2222222222 Simplifying t = -0.2222222222Subproblem 2
Set the factor '(2 + 9t)' equal to zero and attempt to solve: Simplifying 2 + 9t = 0 Solving 2 + 9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9t = 0 + -2 9t = 0 + -2 Combine like terms: 0 + -2 = -2 9t = -2 Divide each side by '9'. t = -0.2222222222 Simplifying t = -0.2222222222Solution
t = {-0.2222222222, -0.2222222222}
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