Question

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

Answer 1

In support of the answer by Mark E

Explanation:

Read his solution up to the point

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

`color(blue)("Solve by factorizing")`

Notice that the numbers `3xx5=15" and "5-3=2`

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

`(-3)xx(+5)`

or

`(+3)xx(-5)`

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

`(x-5)(x+3)=0`

Thus `color(green)(x= +5" and "-3)`

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