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Simplifying 60x2 + 111xz + 24z2 = 0 Reorder the terms: 111xz + 60x2 + 24z2 = 0 Solving 111xz + 60x2 + 24z2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(37xz + 20x2 + 8z2) = 0 Factor a trinomial. 3((4x + z)(5x + 8z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4x + z)' equal to zero and attempt to solve: Simplifying 4x + z = 0 Solving 4x + z = 0 Move all terms containing x to the left, all other terms to the right. Add '-1z' to each side of the equation. 4x + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 4x + 0 = 0 + -1z 4x = 0 + -1z Remove the zero: 4x = -1z Divide each side by '4'. x = -0.25z Simplifying x = -0.25zSubproblem 2
Set the factor '(5x + 8z)' equal to zero and attempt to solve: Simplifying 5x + 8z = 0 Solving 5x + 8z = 0 Move all terms containing x to the left, all other terms to the right. Add '-8z' to each side of the equation. 5x + 8z + -8z = 0 + -8z Combine like terms: 8z + -8z = 0 5x + 0 = 0 + -8z 5x = 0 + -8z Remove the zero: 5x = -8z Divide each side by '5'. x = -1.6z Simplifying x = -1.6zSolution
x = {-0.25z, -1.6z}
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