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

$5x=\sqrt{10+15x}$

Since, we have to solve for x

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

step-1: Take square both sides

$(5x)^2=(\sqrt{10+15x})^2$

$25x^2=10+15x$

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

$x-1=0$

$x=1$

$5x+2=0$

$x=-\frac{2}{5}$

we know that

$x=-\frac{2}{5}$ will make negative value inside sqrt

and we know that negative value inside sqrt is not possible

so,

$x=-\frac{2}{5}$ can not be solution

Hence,

$x=1$................Answer