Question

What is the solution of the equation 5x=sqrt 10+15x?

Answer 1

5x=100+15x
15x-5x= - 100
10x = - 100
x= -100 :10
x= - 10

Answer 2

we are given

`5x=√(10+15x)`

Since, we have to solve for x

To solve for x , we will isolate x on anyone side

step-1: Take square both sides

`(5x)^2=(√(10+15x))^2`

`25x^2=10+15x`

step-2: Move all terms on left side

`25x^2-15x-10=0`

step-3: Factoring

`5(5x^2-3x-2)=0`

`5x^2-3x-2=0`

now, we can factor it

and we get

`(x-1)(5x+2)=0`

step-4: Solve for x

we can set each terms =0

and then we can solve for x

`x-1=0`

`x=1`

`5x+2=0`

`x=-(2)/(5)`

we know that

`x=-(2)/(5)` will make negative value inside sqrt

and we know that negative value inside sqrt is not possible

so,

`x=-(2)/(5)` can not be solution

Hence,

`x=1`................Answer