Question

X^2 - 10x + 9 = 0 Factor and solve

Answer 1

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Answer 2

`{ x }^( 2 )-10x+9`

First you should ask, which two numbers add up to -10 and multiply to 9.

-9 and -1 add up to -10 and multiply to 9.


`(-9)+(-1)=-10`


`(-9)(-1)=9`

So we can factor and rewrite like this ;


`(x-9)\cdot (x-1)`

Let's equal it to 0 again.


`\\ (x-9)\cdot (x-1)=0`

The multiplication of (x-9) and (x-1) is equal to 0

So we should equal them to 0 seperately to find the solution set


`x-9=0\\ \\ x=0+9\\ \\ x=9`

and


`x-1=0\\ \\ x=0+1\\ \\ x=1`

The solution set,


`{ x }_( 1,2 )\quad =\quad \left\{ 9,\quad 1 \right\}`