What is the solution for x if x 13square root x 36Solution

What is the solution for x if x = 13*square root x - 36?

Solution

We\'ll move all terms to one side:

x - 13*sqrt x + 36 = 0

Let sqrt x = t

If we\'ll raise to square both sides, we\'ll get:

x = t^2

We\'ll re-write the equation in t:

t^2 - 13t + 36 = 0

Since the sum is 13 and the product is 36, the roots of the quadratic are t1 = 4 and t2 = 9.

But sqrt x = t1 => sqrt x = 4 => x1 = 4^2

x1 = 16

sqrt x = t2 => sqrt x = 9 => x2 = 9^2

x2 = 81

The solutions of the given equation are: {16 ; 81}.