Any one knows how to solve this maths problem? help?

Question

solve (x+6)^0.5= 6-2(5-x)^0.5 thanks

Answer 1

√(x+6) = 6 - 2√(5-x)

Square both sides:

x + 6 = 36 - 24√(5-x) + 4(5-x)

x + 6 = 56 - 24√(5-x) - 4x

5x - 50 = -24√(5-x)

Square both sides:

25x² - 500x + 2500 = 576(5 - x)

25x² - 500x + 2500 = 2880 - 576x

25x² + 76x - 380 = 0

Using the quadratic formula,

x = [-76 ± √(76² - (4)(25)(-380))]/(2*25)

x = [-76 ± √(43776)]/50

This can be simplified to

x = [-38 ± 6√(304)]/25

or approximately,

x = 2.664543, x = -5.704543

As often happens when we square both sides of an equation, we get a solution that does not satisfy the original equation. You will find that the solution x ≈ -5.704543 does not satisfy the original equation.