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Simplifying 25w2 + -100wz + 100z2 = 0 Reorder the terms: -100wz + 25w2 + 100z2 = 0 Solving -100wz + 25w2 + 100z2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '25'. 25(-4wz + w2 + 4z2) = 0 Factor a trinomial. 25((w + -2z)(w + -2z)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(w + -2z)' equal to zero and attempt to solve: Simplifying w + -2z = 0 Solving w + -2z = 0 Move all terms containing w to the left, all other terms to the right. Add '2z' to each side of the equation. w + -2z + 2z = 0 + 2z Combine like terms: -2z + 2z = 0 w + 0 = 0 + 2z w = 0 + 2z Remove the zero: w = 2z Simplifying w = 2zSubproblem 2
Set the factor '(w + -2z)' equal to zero and attempt to solve: Simplifying w + -2z = 0 Solving w + -2z = 0 Move all terms containing w to the left, all other terms to the right. Add '2z' to each side of the equation. w + -2z + 2z = 0 + 2z Combine like terms: -2z + 2z = 0 w + 0 = 0 + 2z w = 0 + 2z Remove the zero: w = 2z Simplifying w = 2zSolution
w = {2z, 2z}
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