# Solve the equation

• Aug 9th 2010, 12:30 PM
MATNTRNG
Solve the equation
Solve the equation algebraically for all values of x.

8x^3 + 4x^2 - 18x - 9 = 0
• Aug 9th 2010, 12:45 PM
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

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

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

$(2x+1)\left(4x^2+bx-9)$ are the factors, so you only need find "b" and factor the quadratic.
• Aug 9th 2010, 12:47 PM
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.

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

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

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

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

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

• Aug 9th 2010, 12:48 PM
Plato
Quote:

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

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

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