Question

How do you solve `24+x^2=10x`?

Answer 1

You have to pass `10x` to the left hand and equal the quadratic equation to 0
24 + `x^2` `-10x`=0
then you rearrenge it
`x^2` `-10x`+24=0

Then you have to think about two numbers that when you times them you get as the answer 24
and when you add them -10

The numbers are -6 and -4
(-6)x(-4)=24
(-6) +(-4)=-10
The final working is :
`x^2` `-10x`+24=`(x-6)(x-4)`

So the answers are:
`x-6=0`
`x=6`

`x-4=0`
`x=4`

Answer 2

`x=6` or `x=4`

Explanation:

`24+x^2=10x`

Put into standard form, `color(violet)(ax^2+bx+c=0)`

`x^2-10x+24=0`

`darr`Factor using criss-cross method of factoring

`1color(white)(XX)`-6

`1color(white)(XX)`-4

`-4-6`

`=-10` `lArr` same number as our b-value in our rearranged equation.

`:.` `24+x^2=10x` is `color(orange)"(x-6)(x-4)"`

Further on, finding the x-intercepts of `(x-6)(x-4)=0`

`x-6=0` `color(white)(XXXXXX)` and `color(white)(XXXXXX)` `x-4=0`

`x=6` `color(white)(XXXXXXXXXXXXXXXXX)` `x=4`

`:.` the zeros are `color(blue)6` and `color(blue)4`.

Answer 3

`x=6 or x=4`

Explanation:

Here,

`24+x^2=10x`

`=>x^2-10x+24=0`

Now,

`(-6)(-4)=24 and (-6)+(-4)=-10`

So,

`x^2-6x-4x+24=0`

`=>x(x-6)-4(x-6)=0`

`=>(x-6)(x-4)=0`

`=>x-6=0 or x-4=0`

`=>x=6 or x=4`