help with this math problem please!?

Question

solve: (x^3-1)^2-5(x^3-1)-14=0

i need help pleaseee

Answer 1

([x^3-1)+2][(x^3-1)-7]=0
x^3=-1 so x = -1 or x^3 = 8 so x =2

Answer 2

You substitute x^3-1 with let's say y. Now you have y^2-5y-14=0. The solution of this y ecuation is given by y=[5(+/-)sqrt(25+4*1*14)]/2 = [5(+/-)9]/2 = either 7 or -2.
You replace y back with x^3-1 in both cases. First you have x^3-1 = 7 wich means that x^3=8, x=2, second x^3-1 = -2, x = cube root from (-1) = -1.

Answer 3

This is a higher degree quadratic equation.
(x^3-1)^2-5(x^3-1)-14=0

Step 1: Combine exponents
A) (X^2)^2 – X^2 – 14 = 0
B) X^4 – X^2 – 14 = 0 QUADRATIC FORM (Ax^4 – bx^2 –c = 0)

Step 2: Factor the equation
(X^2 – 7) (X^2 + 2) = 0

Step 3: Set each factor equal to zero and solve for X
a) X^2-7=0
X^2= 7
X = sqrt of 7

b) X^2+2=0
X^2= -2
X = sqrt of -2 (this answer is invalid because a neg. number cant have a square root)

Answer X = sqrt of 7

Answer 4

Let z=x^3 - 1.

Then z^2 - 5z - 14 = 0 <=> (z + 2)(z - 7) = 0 <=> z = - 2 or z = 7

=> x^3 - 1 = - 2 <=> x^3 = - 1 <=> x = - 1
or
=> x^3 - 1 = 7 <=> x^3 = 8 <=> x = 2

i.e. Solutions: x = - 1, x = 2.

Answer 5

First let y=x^3-1 then the equation is y^2-5y-14=0
we can factor this by noticing that -14 is -7 times 2 and -5=-7+2 so then y^2-5y-14=(y-7)(y+2)=0 so there are two roots y=7 and y=-2
so we have two equations to solve now x^3-1=7 and x^3-1=-2
which gives us x^3=8 and x^3=-1 taking the cube root gives us x=2 and x=-1. btw this is just the real solutions there are a bunch of complex solutions too.

Answer 6

Expand the polynomials

x^6 - 2x^3 +1 - 5x^3 +6 -14 = 0

x^6 - 7x^3 - 7 = 0

Let u = x^3, then

u^2 -7u - 7 = 0 ---> (u+7)(u-1) = 0 --> u = -7, +1

so

x = cube root (-7) , 1

Note cube root(-7) will have three values (may all be the same)

Answer 7

You need to change variables.
Use X = x^3 - 1
The equation can be rewritten:
X^2 - 5X - 14 = 0
The roots are -2 and 7
therefore x^3 - 1 = -2 or 7 and x^3 = -1 or 8, which means that the roots are -1 and 2 (curt(-1) = -1 and curt(8)=curt(2^3) = 2)