5p^4+8q^4=13p^2*q^2

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Solution for 5p^4+8q^4=13p^2*q^2 equation: 


Simplifying
5p4 + 8q4 = 13p2 * q2

Multiply p2 * q2
5p4 + 8q4 = 13p2q2

Solving
5p4 + 8q4 = 13p2q2

Solving for variable 'p'.

Reorder the terms:
-13p2q2 + 5p4 + 8q4 = 13p2q2 + -13p2q2

Combine like terms: 13p2q2 + -13p2q2 = 0
-13p2q2 + 5p4 + 8q4 = 0

Factor a trinomial.
(5p2 + -8q2)(p2 + -1q2) = 0

Factor a difference between two squares.
(5p2 + -8q2)((p + q)(p + -1q)) = 0


Subproblem 1
Set the factor '(5p2 + -8q2)' equal to zero and attempt to solve:

Simplifying
5p2 + -8q2 = 0

Solving
5p2 + -8q2 = 0

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

Add '8q2' to each side of the equation.
5p2 + -8q2 + 8q2 = 0 + 8q2

Combine like terms: -8q2 + 8q2 = 0
5p2 + 0 = 0 + 8q2
5p2 = 0 + 8q2
Remove the zero:
5p2 = 8q2

Divide each side by '5'.
p2 = 1.6q2

Simplifying
p2 = 1.6q2

Take the square root of each side:
p = {-1.264911064q, 1.264911064q}

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

Simplifying
p + q = 0

Solving
p + q = 0

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

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

Combine like terms: q + -1q = 0
p + 0 = 0 + -1q
p = 0 + -1q
Remove the zero:
p = -1q

Simplifying
p = -1q

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

Simplifying
p + -1q = 0

Solving
p + -1q = 0

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

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

Combine like terms: -1q + q = 0
p + 0 = 0 + q
p = 0 + q
Remove the zero:
p = q

Simplifying
p = q
Solution
p = {-1.264911064q, 1.264911064q, -1q, q}

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