# How do you solve #x^4 - 2x^2 - 8 = 0#?

##### 3 Answers

you should ask yourself what two numbers do you multiply to get -8 and their summation is -2

and that is -4 and +2 so

#### Explanation:

#"make the substitution "u=x^2#

#rArru^2-2u-8=0#

#"the factors of - 8 which sum to - 2 are - 4 and + 2"#

#rArr(u-4)(u+2)=0#

#"equate each factor to zero and solve for u"#

#u-4=0rArru=4#

#u+2=0rArru=-2#

#"change u back into terms of x"#

#u=4rArrx^2=4rArrx=+-2#

#u=-2rArrx^2=-2rArrx=+-sqrt2i#

If x is not explicitly real,

#### Explanation:

Substitute

This is just to make it look less intimidating to factor

Factor:

Substitute back:

Factor:

If you weren't taught imaginary numbers yet, skip the rest of this, you don't need it: