given:
[tex] {x}^{2} + 14x = - 49[/tex]
[tex] {x}^{2} + 14x + 49 = 0[/tex]
this quadratic is easily factored:
[tex](x + 7)(x + 7) = {(x + 7)}^{2} [/tex]
what value of X makes the quadratic equal zero?
[tex]0 = {(x + 7)}^{2} [/tex]
let x = -7
[tex] {( - 7 + 7)}^{2} = 0[/tex]
this is the only value that makes the equation equal to zero.
thus, there is a double root, which is equal to -7
for part 2:
Since it is quadratic, it will always have two roots. This means both roots are equal to -7
generally, whenever a quadratic factors into a perfect square of sums, like:
[tex] {(x + a)}^{2} [/tex]
where 'a' is a constant,
the solution is a double root.
Meaning both roots to the quadratic are equal.
