Posted by **Amy** on Sunday, November 14, 2010 at 8:59pm.

how to solve this equation in the real number system:

2x^(3) + 3x^(2) + 2x + 3 = 0

steps please

- Algebra HELP -
**Henry**, Tuesday, November 16, 2010 at 9:57pm
2X^3 + 3X^2 + 2X + 3 = 0.

First, we reduce the cubic Eq to a guadratic Eq by finding a value of x that satisfies the Eq. This was done by

trial and error. However, the task was made a lot easier by the use of EXCEL Spread sheets.

It was determined x = -1.5 satisfies the cubic Eq:

x = -1.5 = -1 1/2 = -3/2.

x = -3/2,

x + 3/2 = 0,

Multiply both sides by 2 and get:

2x + 3 = 0.

Using long division, we divide the cubic Eq by 2x + 3:

(2x^3 + 3x^2 +2x + 3)/(2x + 3)=

x^2 + 1.

Now we can easily solve the quad. Eq:

x^2 + 1 = 0,

x2 = -1,

x = sqrt(-1) = +- i.

Solution set: x = - 3/2, x = i, x = -i.

So there are 3 solutions which is the max. for a cubic Eq.

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