# How do you solve #2(xsqrt x) + x=8#?

##### 1 Answer

#### Answer:

Can reformulate as a cubic equation:

which has an irrational root findable using Cardano's method or similar.

#### Explanation:

Subtract

Square both sides to get:

Note that squaring can introduce spurious solutions, so we need to check later.

Subtract the right hand side from the left to get:

By the rational roots theorem, the only possible rational roots of this cubic are:

None of these are roots (though

graph{4x^3-x^2+16x-64 [-0.698, 4.302, -1.18, 1.32]}

It is possible to solve

First let

Then:

So

This is of the form

Then you can use Cardano's method to solve, finding a solution of the form:

hence

If you are really interested see: