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Simplifying
(8x + -5z)(8x + 5z) = 0
Multiply (8x + -5z) * (8x + 5z)
(8x * (8x + 5z) + -5z * (8x + 5z)) = 0
((8x * 8x + 5z * 8x) + -5z * (8x + 5z)) = 0
Reorder the terms:
((40xz + 64x2) + -5z * (8x + 5z)) = 0
((40xz + 64x2) + -5z * (8x + 5z)) = 0
(40xz + 64x2 + (8x * -5z + 5z * -5z)) = 0
(40xz + 64x2 + (-40xz + -25z2)) = 0
Reorder the terms:
(40xz + -40xz + 64x2 + -25z2) = 0
Combine like terms: 40xz + -40xz = 0
(0 + 64x2 + -25z2) = 0
(64x2 + -25z2) = 0
Solving
64x2 + -25z2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '25z2' to each side of the equation.
64x2 + -25z2 + 25z2 = 0 + 25z2
Combine like terms: -25z2 + 25z2 = 0
64x2 + 0 = 0 + 25z2
64x2 = 0 + 25z2
Remove the zero:
64x2 = 25z2
Divide each side by '64'.
x2 = 0.390625z2
Simplifying
x2 = 0.390625z2
Take the square root of each side:
x = {-0.625z, 0.625z}
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