# Solve the equation

• Aug 9th 2010, 11:30 AM
MATNTRNG
Solve the equation
Solve the equation algebraically for all values of x.

8x^3 + 4x^2 - 18x - 9 = 0
• Aug 9th 2010, 11:45 AM
Quote:

Originally Posted by MATNTRNG
Solve the equation algebraically for all values of x.

8x^3 + 4x^2 - 18x - 9 = 0

Notice that this is

$\displaystyle (2x)^3+(2x)^2-9(2x)-9=0$

$\displaystyle 2x=-1$ is a solution, so (2x+1) is a factor.

$\displaystyle (2x+1)\left(4x^2+bx-9)$ are the factors, so you only need find "b" and factor the quadratic.
• Aug 9th 2010, 11:47 AM
masters
Quote:

Originally Posted by MATNTRNG
Solve the equation algebraically for all values of x.

8x^3 + 4x^2 - 18x - 9 = 0

Hi MATNTRNG,

First, factor by grouping.

$\displaystyle 8x^3+4x^2-18x-9=0$

$\displaystyle (8x^3+4x^2)-(18x+9)=0$

$\displaystyle 4x^2(2x+1)-9(2x+1)=0$

$\displaystyle (4x^2-9)(2x+1)=0$

I'll bet you can take it from here. Right?

• Aug 9th 2010, 11:48 AM
Plato
Quote:

Originally Posted by MATNTRNG
Solve the equation algebraically for all values of x.

8x^3 + 4x^2 - 18x - 9 = 0

$\displaystyle 8x^3+4x^2-18x-9=4x^2(2x+1)-9(2x+1)$