Find the real or imaginary solutions of each equation by factoring.
x^3+64

Question

Find the real or imaginary solutions of each equation by factoring.
x^3+64

anonymous · Answer

I need someone to walk me through this.

campbell_st · Answer

well this is the sum of 2 cubes

the general form is 

$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$

so you have 

$$x^3 + 4^3$$

when you factor, you get a linear and quadratic factor

so you'll need the general quadratic formula for the the imaginary parts of the quadratic

hope it helps

anonymous · Answer

i did that and when i factored it i got (x-4)(x^2 - 4x +16) i wasn't too sure on how to get the actual solution from there.

campbell_st · Answer

ok... to get solutions you need the factors to equal zero 

so looking at the linear factor you can use 

x + 4 = 0     so x = -4 is a solution 

now the quadratic 

$$x^2 - 4x + 16 = 0$$

you can either use completing the square or the general quadratic formula from here

for completing the square, start with 

$$x^2 - 4x + ? = -16 + ?$$

what do you add to both sides of the equation to complete the square..?

anonymous · Answer

I have it from here. :) thank you. I would rather use the quadratic formula because my calculator helps with that. thank you for your help.