How do you solve $x = sqrtx + 6$ ?

Question

1758 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-20T08:24:46

Substitute $t = sqrt(x)$ to get a quadratic in $t$ . Solve for $t$ , then square to find $x = 9$

Let $t = sqrt(x)$ . Note $t >= 0$ .

Then $t^2 = t + 6$

Subtract $t+6$ from both sides to get:

$0 = t^2 - t - 6 = (t-3)(t+2)$

So $t = 3$ or $t = -2$ .

Discard $t = -2$ since $t$ is the non-negative square root of $x$ .

So $t = 3$ and $x = t^2 = 3^2 = 9$

How do you solve x = sqrtx + 6 x = sqrtx + 6?