Question

I know the answer, I just don't get how you factor the B into 2 variables.

Answer 1

Answer:

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as
`8x^(2) +ax+bx-3`. To find a and b, set up a system to be solved.

`a+b=-2`

`ab=8\left(-3\right)=-24`

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.

`1, -24\\ 2,-12\\ 3,-8\\ 4,-6`

Calculate the sum for each pair.

`1-24=-23\\ 2-12=-10\\ 3-8=-5\\ 4-6=-2`

The solution is the pair that gives sum -2.

`a=-6\\ b=4`

Rewrite
`8x^(2) -2x-3` as (8
`x^(2)` -6x)+(4x-3)

`\left(8x^2-6x\right)+(4x-3)`

Factor out 2x in 8x²-6x.

`2x\left(4x-3\right)+4x-3`

Factor out common term 4x-3 by using distributive property.

`\left(4x-3\right)\left(2x+1\right)`

To find equation solutions, solve 4x-3=0 and 2x+1=0

`x=(3)/(4)\\ x=-(1)/(2)`

I hope this helps you

:)