p^4-11p^2+28=0

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Solution for p^4-11p^2+28=0 equation: 


Simplifying
p4 + -11p2 + 28 = 0

Reorder the terms:
28 + -11p2 + p4 = 0

Solving
28 + -11p2 + p4 = 0

Solving for variable 'p'.

Factor a trinomial.
(4 + -1p2)(7 + -1p2) = 0

Factor a difference between two squares.
((2 + p)(2 + -1p))(7 + -1p2) = 0


Subproblem 1
Set the factor '(7 + -1p2)' equal to zero and attempt to solve:

Simplifying
7 + -1p2 = 0

Solving
7 + -1p2 = 0

Move all terms containing p to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1p2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1p2 = 0 + -7
-1p2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1p2 = -7

Divide each side by '-1'.
p2 = 7

Simplifying
p2 = 7

Take the square root of each side:
p = {-2.645751311, 2.645751311}

Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve:

Simplifying
2 + p = 0

Solving
2 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

Simplifying
p = -2

Subproblem 3
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-2.645751311, 2.645751311, -2, 2}

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