Question

x^3+512=0 please i need to see steps

Answer 1

Is 512 a perfect cube?

Answer 2

\(a^3 - b^3 = (a - b)(b^2 + ab + b^2) \)

Answer 3

okay

Answer 4

512 = 8^3

Answer 5

Sorry, you need the sum of two cubes, not the difference.

\(\large a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)

Answer 6

You have
\(\large x^3 + 8^3 = 0\)
Now just factor following the sum of two cubes pattern just above.

Answer 7

\(\large (x + 8)(x^2 - 8x + 64) = 0 \)

\(\large x + 8 = 0\) or \(\large x^2 - 8x + 64 = 0 \)

Answer 8

The left equation is simple.
Use the quadratic formula on the right equation.

Answer 9

looking for how to breakdown -192

Answer 10

on the root

Answer 11

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

\(x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(64)}}{2(1)} \)

Answer 12

\(x = \dfrac{8 \pm \sqrt{64 - 256}}{2} \)

\(x = \dfrac{8 \pm \sqrt{-192}}{2} \)