Question

Solve for x, given the equation Square root of x plus 9 − 4 = 1.
x = 16, solution is not extraneous

x = 16, solution is extraneous

x = 34, solution is not extraneous

x = 34, solution is extraneous

Answer 1

\[\sqrt{x+9} - 4 = 1\]Is that the equation?

Answer 2

You should at least use parentheses to indicate where the square root ends, such as (square root of (x+9)) - 4 = 1

Answer 3

As a first step, add 4 to both sides:
\[\sqrt{x+9} - 4 + 4 = 1 + 4\]\[\sqrt{x+9} = 5\]So we know that 5 is the square root of 25, because 5*5 = 25, so \(x+9\) must equal 25. What value of \(x\) will make \(x+9 = 25\)?

Answer 4

As far as the extraneous/not extraneous distinction, we substitute our answer back into the original equation and see if it works. If it does, the solution is not extraneous. If it does not work (we get some nonsense like \(1 = 0\)) then that solution is extraneous.

Answer 5

@whpalmer4 so it would be x=16 not extraneous?

Answer 6

Let's check:

\[\sqrt{x+9}-4=1\]\[\sqrt{16+9}-4=1\]\[\sqrt{25}-4=1\]\[5-4=1\]\[1=1\]That looks like a valid solution.