Question #f0544

1 Answer
Sep 15, 2017

Answer:

#x = -1/3#

#x= 3/8#

Explanation:

You want to get all terms on the same side, with the term with the highest degree being positive #(24x^2)#.

So the new equation looks like

#24x^2 - x -3 = 0#

Since you cannot factor anything, you have to use the AC method (multiplying the A times the C). You then have to figure out what two numbers multiply to your product of your AC, and add up to your B #(-x)#.

Those numbers are #8# and #9#, more specifically, positive #8# and #- 9#. You then replace your B with your to multiples of AC, so your new problem is:

#24x^2 -9x + 8x -3 = 0#

Now put them in their respective pairs

#(24x^2-9x) + (8x -3) = 0#

Now factor out the GCF (Greatest Common Factor) possible, your two sets of parenthesis should be exactly the same! Your new equation is

#3x(8x -3) + (8x- 3) = 0#

Since there is an imaginary 1 in front of the second set of parenthesis, don't forget about it! Now put the GCF's in one set of parentheses and the current set of parentheses in another.

#(3x+1) (8x-3) = 0#

Set each set of parentheses equal to zero, and solve for #x#, those are your zeros/solutions/x-intercepts/etc.

P.S. - To check if you're right, you ca FOIL out the binomials and see if you get the original problem, if so, congratulations, if not, maybe try again :D!