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Simplifying (2x + -5z)(5x + -7z) = 0 Multiply (2x + -5z) * (5x + -7z) (2x * (5x + -7z) + -5z * (5x + -7z)) = 0 ((5x * 2x + -7z * 2x) + -5z * (5x + -7z)) = 0 Reorder the terms: ((-14xz + 10x2) + -5z * (5x + -7z)) = 0 ((-14xz + 10x2) + -5z * (5x + -7z)) = 0 (-14xz + 10x2 + (5x * -5z + -7z * -5z)) = 0 (-14xz + 10x2 + (-25xz + 35z2)) = 0 Reorder the terms: (-14xz + -25xz + 10x2 + 35z2) = 0 Combine like terms: -14xz + -25xz = -39xz (-39xz + 10x2 + 35z2) = 0 Solving -39xz + 10x2 + 35z2 = 0 Solving for variable 'x'. Factor a trinomial. (2x + -5z)(5x + -7z) = 0Subproblem 1
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 = 2.5zSubproblem 2
Set the factor '(5x + -7z)' equal to zero and attempt to solve: Simplifying 5x + -7z = 0 Solving 5x + -7z = 0 Move all terms containing x to the left, all other terms to the right. Add '7z' to each side of the equation. 5x + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 5x + 0 = 0 + 7z 5x = 0 + 7z Remove the zero: 5x = 7z Divide each side by '5'. x = 1.4z Simplifying x = 1.4zSolution
x = {2.5z, 1.4z}
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