Let's simplify the given equation step by step:
(X-5)™ + 2x(x-3) = (x™-10x+25)
Expanding the terms on the left side(X-5)(X-5) + 2x(x-3) = (x™-10x+25(X^2 - 5X - 5X + 25) + 2x^2 - 6x = (x™-10x+25(X^2 - 10X + 25) + 2x^2 - 6x = x^2 - 10x + 25
Now simplify the terms and combine like termsX^2 - 10X + 25 + 2x^2 - 6x = x^2 - 10x + 23x^2 - 16x + 25 = x^2 - 10x + 25
Combine the x^2 terms on both sides3x^2 - x^2 - 16x + 10x + 25 = 25
Simplify2x^2 - 6x = 0
Factor2x(x - 3) = 0
Set each factor to zero2x = 0 or x - 3 = 0
Solve for xx = 0 or x = 3
Therefore, the solutions to the original equation are x = 0 and x = 3.
Let's simplify the given equation step by step:
(X-5)™ + 2x(x-3) = (x™-10x+25)
Expanding the terms on the left side
(X-5)(X-5) + 2x(x-3) = (x™-10x+25
(X^2 - 5X - 5X + 25) + 2x^2 - 6x = (x™-10x+25
(X^2 - 10X + 25) + 2x^2 - 6x = x^2 - 10x + 25
Now simplify the terms and combine like terms
X^2 - 10X + 25 + 2x^2 - 6x = x^2 - 10x + 2
3x^2 - 16x + 25 = x^2 - 10x + 25
Combine the x^2 terms on both sides
3x^2 - x^2 - 16x + 10x + 25 = 25
Simplify
2x^2 - 6x = 0
Factor
2x(x - 3) = 0
Set each factor to zero
2x = 0 or x - 3 = 0
Solve for x
x = 0 or x = 3
Therefore, the solutions to the original equation are x = 0 and x = 3.