Verified answer

x+4√x=45

4√x=45-x

16x=x2-90x+2025

0=x2-106x+2025

0=(x-25) (x-81)

x=25, discard x=81

x+4√x=45

ok take the x on the RHS of the equation

you get

4√x = 45 -x

square both sides

you get

16x = 2025 +x^2 -90x

x^2 - 106x + 2025 = 0

(x-25)(x-81) = 0

If you put 81 in the orignal equation , the solution cannot be obtained hence 25 is your answer

x + 4√x = 45 (subtract x from both sides)

4√x = 45 - x (square both sides)

16x = x^2 - 90x + 2025 (subtract 16x from both sides)

0 = x^2 - 106x + 2025 (factor)

0 = (x - 81)(x - 25)

x - 81 = 0 or x - 25 = 0

x = 81 or x = 25

Check:

x + 4√x = 45

81 + 4√81 = 45

81 + 4(9) = 45

117 = 45 (false, so 81 is not a solution)

x + 4√x = 45

25 + 4√25 = 45

25 + 4(5) = 45

45 = 45 (true)

ANSWER: x = 25