Find all real solutions and show work:
2x^3-3x^2+18x-27=0

Given:

The given equation is

To find:

All the real solutions.

Solution:

We have,

It can be written as

Using zero product property, we get

and

and

and

We know that is an imaginary number because there is a negative sign under the square root.

Therefore, is the only real solution of the given equation.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

answer: 1, 3 and 5 are correct

step-by-step explanation: