SOLUTION: Solve the equation {{{8x^3+4x^2-18x-9=0}}} algebraically for all values of x. We've been trying to solve this problem for hours, but it can't be factored at all.

Algebra ->  Equations -> SOLUTION: Solve the equation {{{8x^3+4x^2-18x-9=0}}} algebraically for all values of x. We've been trying to solve this problem for hours, but it can't be factored at all.      Log On


   

Question 293591: Solve the equation 8x%5E3%2B4x%5E2-18x-9=0 algebraically for all values of x.
We've been trying to solve this problem for hours, but it can't be factored at all.
Found 3 solutions by nerdybill, jim_thompson5910, scott8148:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
8x%5E3%2B4x%5E2-18x-9=0
.
Group terms:
%288x%5E3%2B4x%5E2%29-%2818x%2B9%29=0
.
4x%5E2%282x%2B1%29-9%282x%2B1%29=0
.
%282x%2B1%29%284x%5E2-9%29=0
.
Set each term to zero:
2x+1 = 0
2x = -1
x = -1/2
.
4x^2-9 = 0
4x^2 = 9
x^2 = 9/4
x = +- 3/2
.
x = {-3/2, -1/2, 3/2}

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8x%5E3%2B4x%5E2-18x-9 Start with the given expression


%288x%5E3%2B4x%5E2%29%2B%28-18x-9%29 Group like terms


4x%5E2%282x%2B1%29-9%282x%2B1%29 Factor out the GCF 4x%5E2 out of the first group. Factor out the GCF -9 out of the second group


%284x%5E2-9%29%282x%2B1%29 Since we have the common term 2x%2B1, we can combine like terms


%282x%2B3%29%282x-3%29%282x%2B1%29 Now factor 4x%5E2-9 to get %282x%2B3%29%282x-3%29 (difference of squares)


So 8x%5E3%2B4x%5E2-18x-9 factors to %282x%2B3%29%282x-3%29%282x%2B1%29


In other words, 8x%5E3%2B4x%5E2-18x-9=%282x%2B3%29%282x-3%29%282x%2B1%29


This basically means that 8x%5E3%2B4x%5E2-18x-9=0 is equivalent to %282x%2B3%29%282x-3%29%282x%2B1%29=0. I'll let you take it from here.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
hours, huh...

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

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

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

factoring (difference of squares) ___ (2x + 3) (2x - 3) (2x + 1) = 0

x = ±3/2 , -1/2