Решить уравнение: поподробнее , а то не понимаю

Solve for x over the real numbers: x^2-3 x+2 = 2 sqrt(x) (x-1) subtract 2 sqrt(x) (x-1) from both sides: 2-2 sqrt(x) (x-1)-3 x+x^2 = 0 2-2 (x-1) sqrt(x)-3 x+x^2 = 2+2 sqrt(x)-3 x-2 x^(3/2)+x^2: 2+2 sqrt(x)-3 x-2 x^(3/2)+x^2 = 0 simplify and substitute y = sqrt(x): 2+2 sqrt(x)-3 x-2 x^(3/2)+x^2 = 2+2 sqrt(x)-3 (sqrt(x))^2-2 (sqrt(x))^3+(sqrt(x))^4 = y^4-2 y^3-3 y^2+2 y+2 = 0: y^4-2 y^3-3 y^2+2 y+2 = 0 the left hand side factors into a product with three terms: (y-1) (y+1) (y^2-2 y-2) = 0 split into three equations: y-1 = 0 or y+1 = 0 or y^2-2 y-2 = 0 add 1 to both sides: y = 1 or y+1 = 0 or y^2-2 y-2 = 0 substitute back for y = sqrt(x): sqrt(x) = 1 or y+1 = 0 or y^2-2 y-2 = 0 raise both sides to the power of two: x = 1 or y+1 = 0 or y^2-2 y-2 = 0 subtract 1 from both sides: x = 1 or y = -1 or y^2-2 y-2 = 0 substitute back for y = sqrt(x): x = 1 or sqrt(x) = -1 or y^2-2 y-2 = 0 raise both sides to the power of two: x = 1 or x = 1 or y^2-2 y-2 = 0 add 2 to both sides: x = 1 or x = 1 or y^2-2 y = 2 add 1 to both sides: x = 1 or x = 1 or y^2-2 y+1 = 3 write the left hand side as a square: x = 1 or x = 1 or (y-1)^2 = 3 take the square root of both sides: x = 1 or x = 1 or y-1 = sqrt(3) or y-1 = -sqrt(3) add 1 to both sides: x = 1 or x = 1 or y = 1+sqrt(3) or y-1 = -sqrt(3) substitute back for y = sqrt(x): x = 1 or x = 1 or sqrt(x) = 1+sqrt(3) or y-1 = -sqrt(3) raise both sides to the power of two: x = 1 or x = 1 or x = (1+sqrt(3))^2 or y-1 = -sqrt(3) add 1 to both sides: x = 1 or x = 1 or x = (1+sqrt(3))^2 or y = 1-sqrt(3) substitute back for y = sqrt(x): x = 1 or x = 1 or x = (1+sqrt(3))^2 or sqrt(x) = 1-sqrt(3) raise both sides to the power of two: x = 1 or x = 1 or x = (1+sqrt(3))^2 or x = (1-sqrt(3))^2 x^2-3 x+2 => 2-3 1+1^2 = 0 2 (x-1) sqrt(x) => 2 (1-1) sqrt(1) = 0: so this solution is correct x^2-3 x+2 => 2-3 (1-sqrt(3))^2+((1-sqrt(3))^2)^2 = 18-10 sqrt(3) ~~ 0.679492 2 (x-1) sqrt(x) => 2 ((1-sqrt(3))^2-1) sqrt((1-sqrt(3))^2) = 2 (5 sqrt(3)-9) ~~ -0.679492: so this solution is incorrect x^2-3 x+2 => 2-3 (1+sqrt(3))^2+((1+sqrt(3))^2)^2 = 2 (9+5 sqrt(3)) ~~ 35.3205 2 (x-1) sqrt(x) => 2 ((1+sqrt(3))^2-1) sqrt((1+sqrt(3))^2) = 2 (9+5 sqrt(3)) ~~ 35.3205: so this solution is correct the solutions are: answer: | | x = 1 or x = 1 or x = (1+sqrt(3))^2

1) 138 : 115 = 1,2 (м) - 1% плана; 2) 1,2 * 100 = 120 (м) - 100% - столько метров дороги планировали отремонтировать за неделю. ответ: 120 метров.