Question

How do you factor and solve `-1x^2 -2x+35=0`?

Answer 1

`x=5` or `x=-7`

Explanation:

To solve `-1x^2-2x+35=0`, we should first factorize the polynomial `-1x^2-2x+35`

To factorize a quadratic polynomial of type `ax^2+bx+c`,

one needs to split middle term `b` in two parts whose product is `ac`. As in `-1x^2-2x+35`, the product is `-35`, middle term `-2` can be split in `-7` and `5`.

Hence, `-1x^2-2x+35=0` can be written as

`-1x^2-7x+5x+35=0`

or `-x(x+7)+5(x+7)=0`

or `(-x+5)(x+7)=0`

i.e. `-x+5=0` or `x+7=0`

i.e. `x=5` or `x=-7`