Question

`x^2-6x+15=3x-5`?

`x^2 - 6x = 3x-5`

Answer 1

`x=4" or "x=5`

Explanation:

`"assuming you require the solution to the equation"`

`"rearrange "x^2-6x+15=3x-5" into standard form"`

`•color(white)(x)ax^2+bx+c=0;a!=0`

`rArrx^2-9x+20=0`

`"the factors of + 20 which sum to - 9 are - 4 and - 5"`

`rArr(x-4)(x-5)=0`

`"equate each factor to zero and solve for x"`

`x-4=0rArrx=4`

`x-5=0rArrx=5`

Answer 2

`x=5" "` or `" "x = 4`

Explanation:

Given:

`x^2-6x+15 = 3x-5`

Subtract `3x-5` from both sides and transpose to get:

`0 = x^2-9x+20`

To factor this quadratic, we can find a pair of factors of `20` with sum `9`. The pair `5, 4` works in that `5 * 4 = 20` and `5+4 =9`.

So we find:

`0 = x^2-9x+20 = (x-5)(x-4)`

This has zeros `x=5` and `x=4`