Question

How do you solve `h^2=-3h+54`?

Answer 1

`h =-9 or h = 6`

Explanation:

Rearrange to get

`h^2 + 3h - 54 = 0`

Factorise

`( h+ 9)(h - 6) = 0`

`h + 9 = 0 or h- 6 = 0`

`h = - 9 or h =6`

Answer 2

`h=-9" or "h=6`

Explanation:

`"arrange the equation in standard form"`

`rArrh^2+3h-54=0larrcolor(blue)"in standard form"`

`"the factors of - 54 which sum to + 3 are + 9 and - 6"`

`rArr(h+9)(h-6)=0`

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

`h+9=0rArrh=-9`

`h-6=0rArrh=6`

Answer 3

`h = -9, 6`.

Explanation:

We have,

`color(white)(xxx)h^2 = -3h + 54`

`rArr h^2 + 3h - 54 = cancel(-3h) cancel(+ 54) cancel(+ 3h) cancel(- 54)` [Add `3h - 54` to both sides]

`rArr h^2 + 3h - 54 = 0`

`rArr h^2 + (9 - 6)h - 54 = 0` [Break `3` as `9 - 6`]

`rArrh^2 + 9h - 6h - 54 = 0`

`rArr h(h + 9) - 6(h + 9)` [Group Like Terms]

`rArr (h + 9)(h - 6) = 0` [Group Again]

So, If,

`h+ 9 = 0 rArr h = -9`

and if,

`h - 6 = 0 rArr h = 6`

Hence Explained.