How do you solve this polynomial equation?

x^4-6x^3+9x^2=0
x^2(x^2-6x+9)=0
x=0
(x-3)^2=0
x=3

x³ - 6x² + 10x - 2 = x - 2
x³ - 6x² + 9x = 0

x² - 6x + 9 = 0
x² - 3x = - 9 + (- 3)²
x² - 3x = - 9 + 9
(x - 3)² = 0
x - 3 = 0
x = 3

Answer: x = 3, 0

Proof (substitute x with 3):
3^4 - 6(3)³ + 10(3)² - 2(3) = 3² - 2(3)
81 - 6(27) + 10(9) - 6 = 9 - 6
75 - 162 + 90 = 3
3 = 3

i could first enable u=x² and write the equation as u³ - 25u² + 16u - 4 hundred = 0 (it relatively is the derived equation) Any root to this equation could ought to hitch 4 hundred = (2³)(5²) attempt u = 5² = 25 (25)³ - 25(25)² + sixteen(25) - 4 hundred = 0, so u=25 is a root, as a result u-25 is a element. Factoring the u-25 by skill of long branch yields u³ - 25u² + 16u - 4 hundred = (u-25)(u² + sixteen) placing the element u² + sixteen = 0 yields u = 4i, u=-4i So, the answer to the derived equation in u is { 25, -4i, 4i } keep in mind now that u = x², so x = ?u, x = -?u for all of the recommendations above. the answer to the unique equation is as a result { 5, -5, ?(-4i), -?(-4i), ?4i, -?4i } (those are the complicated recommendations) the real recommendations, inspite of the undeniable fact that, are in simple terms { 5, -5 }

x^4 - 6x^3 + 10x^2 - 2x = x^2 - 2x
x^4 - 6x^3 + 10x^2 - x^2 - 2x + 2x = 0
x^4 - 6x^3 + 9x^2 = 0
x^2(x^2 - 6x + 9) = 0
x^2(x^2 - 3x - 3x + 9) = 0
x^2[(x^2 - 3x) - (3x - 9)] = 0
x^2[x(x - 3) - 3(x - 3)] = 0
x^2(x - 3)(x - 3) = 0

x^2 = 0
x = ±√0
x = 0

x - 3 = 0
x = 3

∴ x = 0 , 3

combine like terms, so it'll be:
x^4-6x^3+9x^2= 0

factor out x^2:
x^2 (x^2-6x+9)= 0

x^2 (x-3)(x-3)= 0

x^2= 0
x= 0

x-3= 0
x= 3


x= 0 and 3

x^4-6x^3+10x^2-2X=x^2-2x

+2x and -x^2 so that

x^4-6x^3+9x^2=0

x^2(x^2-6x+9)=0

x^2=0, x=0

x^2-6x+9=0, (x-3)^2=0, x=3

x=0 and 3