Question

Question #9c7c9

Answer 1

`x^2-14x+49=color(blue)((x-7)(x-7)` or `color(blue)((x-7)^2)`

Explanation:

I assumed the `x^*` was meant to be `x^2`

In general `(x+a)(x+b)=x^2+(a+b)x+ab`

In this case
`color(white)("XXX")a+b=-14`
and
`color(white)("XXX")ab=49`

If we consider integer factors (in the hopes of "getting lucky") for `49` we find only
`1xx49`,
`49xx1`,
`7xx7` and
`(-7)xx(-7)`

Comparing these possibilities with the requirement that `a+b=-14`
we find `a=-7` and `b=-7`
So
`(x+a)(x+b)` becomes `(x-7)(x-7)`