How do you solve $sqrt(x+72) = x$ ?

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Answer 1 · 2018-03-24T08:59:57

$x=9$

Square both sides and place terms on one side to get a more familiar quadratic equation:

$x+72 = x^2$

$0=x^2 -x - 72$

It factors to

$(x+8)(x-9)=0$

So the roots are $-8$ and $9$ .

However, we must plug the answers back into the original equation and check.

We see that $-8$ will not work, because only the principal square root is used.

$sqrt(-8+72) = sqrt 64 = 8$ .

$8 != -8" "larr 8$ is an extraneous solution.

So $x=9$ is the only solution:

$sqrt(9+72) = sqrt81 = 9$

$9=9$

How do you solve sqrt(x+72) = xsqrt(x+72) = x?