Question

What are the roots of the polynomial equation x3-7x=6x-12?

Answer 1

This is not a polynomial equation unless one of those is squared.  As it stands x=-.833.  If you can tell me which is squared I can help solve the polynomial.

Ok, that is usually notated as x^3 to be clear.   I'll solve it now.

x^3-13x-12=0

Then use factor theorum to solve x^3-13x-12/x+1 =0
So you get one solution of x+1=0
x=-1

Then you have x^2-x-12 now you complete the square.

Take half of the x-term coefficient and square it. Add this value to both sides. In this example we have:

The x-term coefficient = −1

The half of the x-term coefficient = −1/2

After squaring we have (−1/2)2=1/4

When we add 1/4 to both sides we have:

x2−x+1/4=12+1/4

STEP 3: Simplify right side

x2−x+1/4=49/4

STEP 4: Write the perfect square on the left.

(x−1/2)2=49/4

STEP 5: Take the square root of both sides.

x−1/2=±√49/4

STEP 6: Solve for x.

x=1/2±√49/4

that is,

x1=−3

x2=4

and the one from before 

x=-1

Answer 2

This is not a polynomial equation unless one of those is squared.