Question

Find the real and complex solutions of x^4+12x^2=-27

Answer 1

`x=\pm√(3i) ,\pm3i`

Explanation:

1) Move all terms to one side.

`{x}^(4)+12{x}^(2)+27=0`

2) Factor
`{x}^(4)+12{x}^(2)+27x`.

1) Ask: Which two numbers add up to 12nd multiply to 27?

3 and 9

2) Rewrite the expression using the above.

`({x}^(2)+3)({x}^(2)+9)`

Outcome:
`({x}^(2)+3)({x}^(2)+9)=0`

2) Solve for x.

1)Ask: When will
`({x}^(2)+3)({x}^(2)+9)` equal zero?

When
`{x}^(2)+3=0`or
`{x}^(2)+9=0`

2) Solve each of the 2 equations above.

`x=\pm√(3i) ,\pm3i`

Thanks.