Final Answer
Step-by-step Solution
Specify the solving method
We can try to factor the expression $2\left(\sqrt{x}\right)^2-1-\sqrt{x}$ by applying the following substitution
Substituting in the polynomial, the expression results in
Factor the trinomial $2u^2-1-u$ of the form $ax^2+bx+c$, first, make the product of $2$ and $-1$
Now, find two numbers that multiplied give us $-2$ and add up to $-1$
Rewrite the original expression
Factor $2u^2-1+u-2u$ by the greatest common divisor $2$
Factoring by $u$
Factoring by $u-1$
Replace $u$ with the value that was assigned to it: $\sqrt{x}$
Break the equation in $2$ factors and set each equal to zero, to obtain
Solve the equation ($1$)
We need to isolate the dependent variable , we can do that by simultaneously subtracting $-1$ from both sides of the equation
Multiply $-1$ times $-1$
Removing the variable's exponent raising both sides of the equation to the power of $2$
Solve the equation ($2$)
Combining all solutions, the $2$ solutions of the equation are
Verify that the solutions obtained are valid in the initial equation
The valid solutions to the equation are the ones that, when replaced in the original equation, don't result in any square root of a negative number and make both sides of the equation equal to each other