Question 710177
{{{sqrt(5x) = -5}}}
{{{sqrt(5x)}}} refers to the positive number/expression that, when squared, results in 5x. But the equation says that {{{sqrt(5x)}}} is a negative number, -5. A positive square root cannot be equal to a negative number. IOW: There is <u>no solution</u> to this equation!<br>
If you don't notice this and proceed to solve the equation, as you did, then you can still find out that there is no solution. <i>Any</i> time you square both sides of an equation, as you did, you <i>must</i> check your answers! Let's check your solution, x = 5, using the original equation:
{{{sqrt(5x) = -5}}}
Checking x = 5:
{{{sqrt(5(5)) = -5}}}
{{{sqrt(25) = -5}}}
{{{5 = -5}}}
Since this is false, the check fails!! x=5 is not a solution. And since we must reject the only "solution" you found, there are no solutions to your equation.