Question

How do you solve `x^2+14x + 49= 19`?

Answer 1

`x^2+14x+49=19` has the two solutions `x=-7+-\sqrt19`
(i.e. `x_1=-7-\sqrt19` and `x_2=-7+\sqrt19`)

Explanation:

The first I notice is that `14=2*7`, and `49=7^2`

Please also remember that `(x+a)^2=x^2+2a+a^2`
Therefore `x^2+14x+49=(x+7)^2=19`

It follows, therefore, that
`x+7=+-\sqrt19`

We, therefore, have two values of x here:
`x=-7+-\sqrt19`