Question

How do you solve `h^2 + 10h = -21`?

Answer 1

The solutions are
`color(green)( h = -3 , h = -7`

Explanation:

`h^2 + 10h + 21 = 0`

Here, we can first factorise the expression and then find the solutions:

Factorising by splitting middle term:

`h^2 + 10h + 21 = 0`
`h^2 +color(green)(3h + 7h) + 21 = 0`
`h( h+3) +7( h+3) = 0`
`(h+3)(h+7) = 0`
Equating the factors with zero to obtain solutions:
`h+3 = 0 ,color(green)( h=-3`
`h+7 = 0 , color(green)(h=-7`