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Simplifying
(4x + -2z)(4x + 2z) = 0
Multiply (4x + -2z) * (4x + 2z)
(4x * (4x + 2z) + -2z * (4x + 2z)) = 0
((4x * 4x + 2z * 4x) + -2z * (4x + 2z)) = 0
Reorder the terms:
((8xz + 16x2) + -2z * (4x + 2z)) = 0
((8xz + 16x2) + -2z * (4x + 2z)) = 0
(8xz + 16x2 + (4x * -2z + 2z * -2z)) = 0
(8xz + 16x2 + (-8xz + -4z2)) = 0
Reorder the terms:
(8xz + -8xz + 16x2 + -4z2) = 0
Combine like terms: 8xz + -8xz = 0
(0 + 16x2 + -4z2) = 0
(16x2 + -4z2) = 0
Solving
16x2 + -4z2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4z2' to each side of the equation.
16x2 + -4z2 + 4z2 = 0 + 4z2
Combine like terms: -4z2 + 4z2 = 0
16x2 + 0 = 0 + 4z2
16x2 = 0 + 4z2
Remove the zero:
16x2 = 4z2
Divide each side by '16'.
x2 = 0.25z2
Simplifying
x2 = 0.25z2
Take the square root of each side:
x = {-0.5z, 0.5z}
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