how do you solve for x when:

 

 

 

x^3 + 216 = 0

 

 

 

the answer should be -6, 3 + 3ÃÆâÃâ¹Ã¢â¬Â Ãâ¦Ã¡3i, 3 - 3ÃÆâÃâ¹Ã¢â¬Â Ãâ¦Ã¡3i

 

the checkmark is a root sign

 

 

 

 

 

i know how to get the -6 cause x^3+216=0 factors into (x+6)(x^2-6x+36)=0

 

 

 

but i have no idea how im supposed to get the last two parts (except from looking in the back of the book...but i have to show work, and there's like 15 problems similar to this)

 

 

 

so help = appreciated. if i figure out how to do one of these, i can get the rest

well since imaginary numbers are involved all you have to do is solve it with the quadradic formula right?

ohhhhh yea #-o

no, the quadratic formula is only for quadratics.

 

quadratics are ax^2+bx+c=0

 

that equation has an x^3

 

I would use synthetic division.

after you factor, you have a quadratic equation. the answer came out right so ty xpls for reminding me of that annoying formula lol

I would still use synthetic division in the first place. makes life so much easier \

i have no idea what that is though \ lol

after you factor, you have a quadratic equation. the answer came out right so ty xpls for reminding me of that annoying formula lol

no problem, just helping you help yourself.

I should know this, but it's been about 4 years since I took Algebra 2.

 

 

 

 

 

Btw... this is the part of math that you will hate most lol

im actually in college algebra and trig (we're just doing review) ...and i didn't find algebra 1 and 2 that bad :P

And in case you hadn't seen the factors:

 

 

 

x^3 = -216

 

 

 

(a+bi)^3 = -216

 

 

 

1) Real part: a^3-3ab^2 = -216

 

AND

 

2) Imaginary part: 3ba^2-b^3 = 0

 

 

 

From 2)

 

3) b^3 = 3ba^2

 

b^2 = 3a^2

 

 

 

From 1) and 3)

 

4) a^3-3ab^2 = -216

 

a^3-9a^3 = -216

 

8a^3=216

 

a^3=27

 

a=3

 

 

 

From 3) and 4)

 

b^2 = 3a^2

 

b = 3ÃÆâÃâ¹Ã¢â¬Â Ãâ¦Ã¡3 OR -3ÃÆâÃâ¹Ã¢â¬Â Ãâ¦Ã¡3

 

 

 

Thus 3+3ÃÆâÃâ¹Ã¢â¬Â Ãâ¦Ã¡3i and 3-3ÃÆâÃâ¹Ã¢â¬Â Ãâ¦Ã¡3i are solutions too. ^^

right...lol

 

 

 

 

 

quadratic formula ftw!

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