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Simplifying 8y2 + 38yz + -10z2 = 0 Reorder the terms: 38yz + 8y2 + -10z2 = 0 Solving 38yz + 8y2 + -10z2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(19yz + 4y2 + -5z2) = 0 Factor a trinomial. 2((4y + -1z)(y + 5z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4y + -1z)' equal to zero and attempt to solve: Simplifying 4y + -1z = 0 Solving 4y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 4y + -1z + z = 0 + z Combine like terms: -1z + z = 0 4y + 0 = 0 + z 4y = 0 + z Remove the zero: 4y = z Divide each side by '4'. y = 0.25z Simplifying y = 0.25zSubproblem 2
Set the factor '(y + 5z)' equal to zero and attempt to solve: Simplifying y + 5z = 0 Solving y + 5z = 0 Move all terms containing y to the left, all other terms to the right. Add '-5z' to each side of the equation. y + 5z + -5z = 0 + -5z Combine like terms: 5z + -5z = 0 y + 0 = 0 + -5z y = 0 + -5z Remove the zero: y = -5z Simplifying y = -5zSolution
y = {0.25z, -5z}
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