Answer:
Answer:
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as [tex]8x^{2} +ax+bx-3[/tex]. To find a and b, set up a system to be solved.
[tex]a+b=-2[/tex]
[tex]ab=8\left(-3\right)=-24[/tex]
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -24.
[tex]1, -24\\ 2,-12\\ 3,-8\\ 4,-6[/tex]
Calculate the sum for each pair.
[tex]1-24=-23\\ 2-12=-10\\ 3-8=-5\\ 4-6=-2[/tex]
The solution is the pair that gives sum -2.
[tex]a=-6\\ b=4[/tex]
Rewrite [tex]8x^{2} -2x-3[/tex] as (8[tex]x^{2}[/tex] -6x)+(4x-3)
[tex]\left(8x^2-6x\right)+(4x-3)[/tex]
Factor out 2x in 8x²-6x.
[tex]2x\left(4x-3\right)+4x-3[/tex]
Factor out common term 4x-3 by using distributive property.
[tex]\left(4x-3\right)\left(2x+1\right)[/tex]
To find equation solutions, solve 4x-3=0 and 2x+1=0
[tex]x=\frac{3}{4}\\ x=-\frac{1}{2}[/tex]
I hope this helps you
:)
