Question

How do you factor and solve `x^2-16=6x`?

Answer 1

`x=-2, 8`

Explanation:

1) Rearrange into the form`" "ax^2+bx+c=0`

2) Factorise

3) Put each bracket `=0` and solve each bracket

1) Rearrange

`x^2-16=6x`

subtract `6x` from both sides

`x^2-16-6x=6x-6x`

`x^2-16-6x=0`

`x^2-6x-16=0`

2) Factorise

`x^2-6x-16=0`

a) `"because it is an " x^2 " equation, the brackets will be of the form " (x+-" ")(x+-" ")`

we now need to find the two numbers for the brackets.

`x^2color(red)(-6)xcolor(blue)(-16)=0`

we need two numbers that multiply to `color(blue)(-16)`, but add to `color(red)(-6)`

by trial and error:

`-16xx1=-16=>-16+ 1=-15" X"`

`-8xx2=-16=>-8+ 2=--6" sqrt`

so the brackets now become;

`(x-8)(x+2)=0`

3) Solve

`x-8=0=>x=8`

`x+2=0=>x=-2`

`:.x=-2, 8`