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Simplifying 10x2 + 3xz + -18z2 = 0 Reorder the terms: 3xz + 10x2 + -18z2 = 0 Solving 3xz + 10x2 + -18z2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -6z)(2x + 3z) = 0Subproblem 1
Set the factor '(5x + -6z)' equal to zero and attempt to solve: Simplifying 5x + -6z = 0 Solving 5x + -6z = 0 Move all terms containing x to the left, all other terms to the right. Add '6z' to each side of the equation. 5x + -6z + 6z = 0 + 6z Combine like terms: -6z + 6z = 0 5x + 0 = 0 + 6z 5x = 0 + 6z Remove the zero: 5x = 6z Divide each side by '5'. x = 1.2z Simplifying x = 1.2zSubproblem 2
Set the factor '(2x + 3z)' equal to zero and attempt to solve: Simplifying 2x + 3z = 0 Solving 2x + 3z = 0 Move all terms containing x to the left, all other terms to the right. Add '-3z' to each side of the equation. 2x + 3z + -3z = 0 + -3z Combine like terms: 3z + -3z = 0 2x + 0 = 0 + -3z 2x = 0 + -3z Remove the zero: 2x = -3z Divide each side by '2'. x = -1.5z Simplifying x = -1.5zSolution
x = {1.2z, -1.5z}
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