# How do you solve 2sqrt(x+4) -1=x and find any extraneous solutions?

Aug 19, 2016

In support of the answer by Mark E

#### Explanation:

Read his solution up to the point

Now Simplify:
${x}^{2} - 2 x - 15 = 0$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
With quadratics if you can not spot the factorisation then it is wise to solve using the formula or completing the square.

$\textcolor{b l u e}{\text{Solve by factorizing}}$

Notice that the numbers $3 \times 5 = 15 \text{ and } 5 - 3 = 2$

The 15 is negative in the given equation so we must have either

$\left(- 3\right) \times \left(+ 5\right)$

or

$\left(+ 3\right) \times \left(- 5\right)$

'.....................................................................
The $2 x$ is negative so the larger number of the subtraction has to be negative. Giving: $3 - 5$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus we have:

$\left(x - 5\right) \left(x + 3\right) = 0$

Thus $\textcolor{g r e e n}{x = + 5 \text{ and } - 3}$

Returning to Mark E's solution shows that -3 is not a valid solution
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~