Solve z+(16/z+2)=6

Evaluate

z + (\frac{16}{z} + 2) = 6

Remove the parentheses

z + \frac{16}{z} + 2 = 6

Multiply both sides of the equation by LCD

(z + \frac{16}{z} + 2) z = 6 z

Simplify the equation

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z^{2} + 16 + 2 z = 6 z

Move the expression to the left side

z^{2} + 16 + 2 z - 6 z = 0

Subtract the terms

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z^{2} + 16 - 4 z = 0

Rewrite in standard form

z^{2} - 4 z + 16 = 0

Substitute a= 1,b= - 4 and c= 16 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 16}{2}

Simplify the expression

More Steps

z = \frac{4 \pm - 48}{2}

Solution

z \in / R

Alternative Form

No real solution

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