# Solve for x. 2x^4 +3 = 165

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Given `2x^4+3=165`

or, `2x^4=165-3`

or, `2x^4=162`

or, `x^4=162/2=81`

or, `x^4-81=0`

or, `x^4-3^4=0`

or, `(x^2-3^2)(x^2+3^2)=0`

As `x^2-a^2=(x-a)(x+a)` .

or, `(x-3)(x+3)(x+3i)(x-3i)=0`

`(x-3)=0rArrx=3` , `(x+3)=0rArrx=-3` ,

`(x+3i)=0rArrx=-3i,` `(x-3i)=0rArr x=3i` .

So, `x=+-3` and `x=+-3i` .

The equation 2x^4 +3 = 165 has to be solved for x.

2x^4 +3 = 165

=> 2x^4 + 3 - 3 = 165 - 3

=> 2x^4 = 162

=> x^4 = 81

=> `x^2 = +-9`

For x^2 = 9, `x = +-3`

For x^2 = -9, `x = +-3*i`

**The solutions of the equation are **`{-3*i, 3*i, -3, 3}`