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Simplifying -6x2 + 19xz + -10z2 = 0 Reorder the terms: 19xz + -6x2 + -10z2 = 0 Solving 19xz + -6x2 + -10z2 = 0 Solving for variable 'x'. Factor a trinomial. (-3x + 2z)(2x + -5z) = 0Subproblem 1
Set the factor '(-3x + 2z)' equal to zero and attempt to solve: Simplifying -3x + 2z = 0 Solving -3x + 2z = 0 Move all terms containing x to the left, all other terms to the right. Add '-2z' to each side of the equation. -3x + 2z + -2z = 0 + -2z Combine like terms: 2z + -2z = 0 -3x + 0 = 0 + -2z -3x = 0 + -2z Remove the zero: -3x = -2z Divide each side by '-3'. x = 0.6666666667z Simplifying x = 0.6666666667zSubproblem 2
Set the factor '(2x + -5z)' equal to zero and attempt to solve: Simplifying 2x + -5z = 0 Solving 2x + -5z = 0 Move all terms containing x to the left, all other terms to the right. Add '5z' to each side of the equation. 2x + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 2x + 0 = 0 + 5z 2x = 0 + 5z Remove the zero: 2x = 5z Divide each side by '2'. x = 2.5z Simplifying x = 2.5zSolution
x = {0.6666666667z, 2.5z}
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