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Simplifying 100t3 + -40wt2 + 4w2t = 0 Reorder the terms: 4tw2 + -40t2w + 100t3 = 0 Solving 4tw2 + -40t2w + 100t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t'. 4t(w2 + -10tw + 25t2) = 0 Factor a trinomial. 4t((w + -5t)(w + -5t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(w + -5t)' equal to zero and attempt to solve: Simplifying w + -5t = 0 Reorder the terms: -5t + w = 0 Solving -5t + w = 0 Move all terms containing t to the left, all other terms to the right. Add '-1w' to each side of the equation. -5t + w + -1w = 0 + -1w Combine like terms: w + -1w = 0 -5t + 0 = 0 + -1w -5t = 0 + -1w Remove the zero: -5t = -1w Divide each side by '-5'. t = 0.2w Simplifying t = 0.2wSubproblem 3
Set the factor '(w + -5t)' equal to zero and attempt to solve: Simplifying w + -5t = 0 Reorder the terms: -5t + w = 0 Solving -5t + w = 0 Move all terms containing t to the left, all other terms to the right. Add '-1w' to each side of the equation. -5t + w + -1w = 0 + -1w Combine like terms: w + -1w = 0 -5t + 0 = 0 + -1w -5t = 0 + -1w Remove the zero: -5t = -1w Divide each side by '-5'. t = 0.2w Simplifying t = 0.2wSolution
t = {0, 0.2w, 0.2w}
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