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Simplifying 45w2 + 150wt + 125t2 = 0 Reorder the terms: 150tw + 125t2 + 45w2 = 0 Solving 150tw + 125t2 + 45w2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(30tw + 25t2 + 9w2) = 0 Factor a trinomial. 5((5t + 3w)(5t + 3w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5t + 3w)' equal to zero and attempt to solve: Simplifying 5t + 3w = 0 Solving 5t + 3w = 0 Move all terms containing t to the left, all other terms to the right. Add '-3w' to each side of the equation. 5t + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 5t + 0 = 0 + -3w 5t = 0 + -3w Remove the zero: 5t = -3w Divide each side by '5'. t = -0.6w Simplifying t = -0.6wSubproblem 2
Set the factor '(5t + 3w)' equal to zero and attempt to solve: Simplifying 5t + 3w = 0 Solving 5t + 3w = 0 Move all terms containing t to the left, all other terms to the right. Add '-3w' to each side of the equation. 5t + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 5t + 0 = 0 + -3w 5t = 0 + -3w Remove the zero: 5t = -3w Divide each side by '5'. t = -0.6w Simplifying t = -0.6wSolution
t = {-0.6w, -0.6w}
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