x2 5x squareroot x2 5x 2 4SolutionNot clear what you as

x^2 - 5x - squareroot x^2 - 5x - 2 = 4

Not clear what you asking for still I am just solving the equation

x² -5x -sqrt(x² -5x -2) = 4 -----------------------(1)

take x² -5x -2 = u => x² -5x = u+2, rewrite (1) as

u+2 -sqrt(u) = 4

=>u-2 = sqrt(u)

=> (u-2)² = u

=> u² -4u +4 = u

=> u² -5u +4 =0

=> u² -(4+1)u +4 =0

=> (u-4)(u-1) = 0 => u=4 and u =1

for u = 4

x² -5x -2 =4

=>x² -5x -6 =0

=> x² -(6-1)x -6 =0

=> (x+6)(x-1) =0 => x= -6 and x=1

for u =1

x² -5x -2 = 1

=> x² -5x - 3= 0

using x = (-b +- sqrt(b² -4ac))/2a gives

x = (-(-5) +-sqrt(25 -4 *1 *(-3)))/2

= (5 + - sqrt(37))/2

hence x = (5+sqrt(37))/2 and (5-sqrt(37))/2