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Simplifying (4x + -1z)(4x + -7z) = 0 Multiply (4x + -1z) * (4x + -7z) (4x * (4x + -7z) + -1z * (4x + -7z)) = 0 ((4x * 4x + -7z * 4x) + -1z * (4x + -7z)) = 0 Reorder the terms: ((-28xz + 16x2) + -1z * (4x + -7z)) = 0 ((-28xz + 16x2) + -1z * (4x + -7z)) = 0 (-28xz + 16x2 + (4x * -1z + -7z * -1z)) = 0 (-28xz + 16x2 + (-4xz + 7z2)) = 0 Reorder the terms: (-28xz + -4xz + 16x2 + 7z2) = 0 Combine like terms: -28xz + -4xz = -32xz (-32xz + 16x2 + 7z2) = 0 Solving -32xz + 16x2 + 7z2 = 0 Solving for variable 'x'. Factor a trinomial. (4x + -7z)(4x + -1z) = 0Subproblem 1
Set the factor '(4x + -7z)' equal to zero and attempt to solve: Simplifying 4x + -7z = 0 Solving 4x + -7z = 0 Move all terms containing x to the left, all other terms to the right. Add '7z' to each side of the equation. 4x + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 4x + 0 = 0 + 7z 4x = 0 + 7z Remove the zero: 4x = 7z Divide each side by '4'. x = 1.75z Simplifying x = 1.75zSubproblem 2
Set the factor '(4x + -1z)' equal to zero and attempt to solve: Simplifying 4x + -1z = 0 Solving 4x + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add 'z' to each side of the equation. 4x + -1z + z = 0 + z Combine like terms: -1z + z = 0 4x + 0 = 0 + z 4x = 0 + z Remove the zero: 4x = z Divide each side by '4'. x = 0.25z Simplifying x = 0.25zSolution
x = {1.75z, 0.25z}
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