math is haaaaaaaard ;-;

51:

 

Solve for x:
x^4-5 x^3+15 x^2-45 x+54 = 0

The left hand side factors into a product with three terms:
(x-3) (x-2) (x^2+9) = 0

Split into three equations:
x-3 = 0 or x-2 = 0 or x^2+9 = 0

Add 3 to both sides:
x = 3 or x-2 = 0 or x^2+9 = 0

Add 2 to both sides:
x = 3 or x = 2 or x^2+9 = 0

Subtract 9 from both sides:
x = 3 or x = 2 or x^2 = -9

Take the square root of both sides:
Answer: |x = 3    or    x = 2    or    x = 3i    or    x = -3i

 

52:

 

Solve for x:
2 x^4+5 x^3-10 x^2+10 x+8 = 0

The left hand side factors into a product with three terms:
(x+4) (2 x+1) (x^2-2 x+2) = 0

Split into three equations:
x+4 = 0 or 2 x+1 = 0 or x^2-2 x+2 = 0

Subtract 4 from both sides:
x = -4 or 2 x+1 = 0 or x^2-2 x+2 = 0

Subtract 1 from both sides:
x = -4 or 2 x = -1 or x^2-2 x+2 = 0

Divide both sides by 2:
x = -4 or x = -1/2 or x^2-2 x+2 = 0

Subtract 2 from both sides:
x = -4 or x = -1/2 or x^2-2 x = -2

Add 1 to both sides:
x = -4 or x = -1/2 or x^2-2 x+1 = -1

Write the left hand side as a square:
x = -4 or x = -1/2 or (x-1)^2 = -1

Take the square root of both sides:
x = -4 or x = -1/2 or x-1 = i or x-1 = -i

Add 1 to both sides:
x = -4 or x = -1/2 or x = 1+i or x-1 = -i

Add 1 to both sides:
Answer: |x = -4    or    x = -1/2    or    x = 1+i    or    x = 1-i

Here are a couple of links to help you with the problem...

https://www.youtube.com/watch?v=xY7Vpxvm62A

https://www.khanacademy.org/math/algebra2/polynomial-functions/advanced-polynomial-factorization-methods/v/factoring-5th-degree-polynomial-to-find-real-zeros