Question

How do you solve `12 = 2x^2 - 5x`?

Answer 1

`x=-3/2" or "x=4`

Explanation:

`"rearrange the equation into "color(blue)"standard form"`

`rArr2x^2-5x-12=0larrcolor(blue)"in standard form"`

`"factorise using the a-c method"`

`"that is factors of the product "2xx-12=-24`
`"which sum to - 5"`

`"the factors required are - 8 and + 3"`

`"'split' the middle term using these factors"`

`rArr2x^2-8x+3x-12=0larrcolor(blue)"factor by grouping"`

`rArrcolor(red)(2x)(x-4)color(red)(+3)(x-4)=0`

`"take out the common factor "(x-4)`

`rArr(x-4)(color(red)(2x+3))=0`

`"equate each factor to zero and solve for x"`

`x-4=0rArrx=4`

`2x+3=0rArrx=-3/2`