中學數學: 100√x =1200+2x 請列詳細步驟

100√x =1200+2x
1200+2x - 100√x = 0
2x - 100√x + 1200 = 0
x - 50√x + 600 = 0
(√x)^2 - 50√x + 600 = 0 (This is a quadratic equation)
Factorize
(√x - 30)(√x - 20) = 0
√x = 30 or √x = 20
x = 30^2 = 900
x = 20^2 = 400

x = 400 or 900 (answer)

Check:
100√400 =1200+2(400)
100(20) =1200+800
2000 =2000

100√900 =1200+2(900)
100(30) =1200+1800
3000 =3000

Hint: square the both sides.