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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation to be solved is x=13square root x-36

x=13square root x-36

=> x = 13*sqrt x - 36

=> x + 36 = 13*sqrt x

square both the sides

=> x^2 + 36^2 + 72x = 13^2*x

=> x^2 -97x + 1296 = 0

=> x^2 - 16x - 81x + 1296 = 0

=> x(x - 16) - 81(x - 16) = 0

=> (x - 16)(x - 81) = 0

x = 16 and x = 81

The solution of the equation is x = 16 and x = 81

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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}.

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