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Simplifying z2 + 8zw + 15w2 = 0 Reorder the terms: 8wz + 15w2 + z2 = 0 Solving 8wz + 15w2 + z2 = 0 Solving for variable 'w'. Factor a trinomial. (5w + z)(3w + z) = 0Subproblem 1
Set the factor '(5w + z)' equal to zero and attempt to solve: Simplifying 5w + z = 0 Solving 5w + z = 0 Move all terms containing w to the left, all other terms to the right. Add '-1z' to each side of the equation. 5w + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 5w + 0 = 0 + -1z 5w = 0 + -1z Remove the zero: 5w = -1z Divide each side by '5'. w = -0.2z Simplifying w = -0.2zSubproblem 2
Set the factor '(3w + z)' equal to zero and attempt to solve: Simplifying 3w + z = 0 Solving 3w + z = 0 Move all terms containing w to the left, all other terms to the right. Add '-1z' to each side of the equation. 3w + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 3w + 0 = 0 + -1z 3w = 0 + -1z Remove the zero: 3w = -1z Divide each side by '3'. w = -0.3333333333z Simplifying w = -0.3333333333zSolution
w = {-0.2z, -0.3333333333z}
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