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Simplifying -60w2 + -550wz + 500z2 = 0 Reorder the terms: -550wz + -60w2 + 500z2 = 0 Solving -550wz + -60w2 + 500z2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '10'. 10(-55wz + -6w2 + 50z2) = 0 Factor a trinomial. 10((-1w + -10z)(6w + -5z)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1w + -10z)' equal to zero and attempt to solve: Simplifying -1w + -10z = 0 Solving -1w + -10z = 0 Move all terms containing w to the left, all other terms to the right. Add '10z' to each side of the equation. -1w + -10z + 10z = 0 + 10z Combine like terms: -10z + 10z = 0 -1w + 0 = 0 + 10z -1w = 0 + 10z Remove the zero: -1w = 10z Divide each side by '-1'. w = -10z Simplifying w = -10zSubproblem 2
Set the factor '(6w + -5z)' equal to zero and attempt to solve: Simplifying 6w + -5z = 0 Solving 6w + -5z = 0 Move all terms containing w to the left, all other terms to the right. Add '5z' to each side of the equation. 6w + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 6w + 0 = 0 + 5z 6w = 0 + 5z Remove the zero: 6w = 5z Divide each side by '6'. w = 0.8333333333z Simplifying w = 0.8333333333zSolution
w = {-10z, 0.8333333333z}
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