Question

X^2-7x-34=10 solve this equation using factorising and soling quadratics

Answer 1

`x=-7; x=11`

Explanation:

Let's bring 10 to the LHS first.

`x^2-7x-44=0`.

At this point we need two numbers that add to -7 and multiply to -44. From the signs we can tell that the greater of the two is negative, and the smaller is positive. Furthermore, since
`44=11* 4` we found our two suspects: -11 and 4 (which indeed add up to -7)

Now we can factorize the equation as

`(x-11)(x+4) =0`

which tells us that either
`x-11=0 \rightarrow x=11` or
`x+7=0 \rightarrow x=-7`