9a^4-7a^2b^2-50b^4=0

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Solution for 9a^4-7a^2b^2-50b^4=0 equation: 


Simplifying
9a4 + -7a2b2 + -50b4 = 0

Reorder the terms:
-7a2b2 + 9a4 + -50b4 = 0

Solving
-7a2b2 + 9a4 + -50b4 = 0

Solving for variable 'a'.

Factor a trinomial.
(9a2 + -25b2)(a2 + 2b2) = 0

Factor a difference between two squares.
((3a + 5b)(3a + -5b))(a2 + 2b2) = 0


Subproblem 1
Set the factor '(a2 + 2b2)' equal to zero and attempt to solve:

Simplifying
a2 + 2b2 = 0

Solving
a2 + 2b2 = 0

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

Add '-2b2' to each side of the equation.
a2 + 2b2 + -2b2 = 0 + -2b2

Combine like terms: 2b2 + -2b2 = 0
a2 + 0 = 0 + -2b2
a2 = 0 + -2b2
Remove the zero:
a2 = -2b2

Simplifying
a2 = -2b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3a + 5b)' equal to zero and attempt to solve:

Simplifying
3a + 5b = 0

Solving
3a + 5b = 0

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

Add '-5b' to each side of the equation.
3a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
3a + 0 = 0 + -5b
3a = 0 + -5b
Remove the zero:
3a = -5b

Divide each side by '3'.
a = -1.666666667b

Simplifying
a = -1.666666667b

Subproblem 3
Set the factor '(3a + -5b)' equal to zero and attempt to solve:

Simplifying
3a + -5b = 0

Solving
3a + -5b = 0

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

Add '5b' to each side of the equation.
3a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
3a + 0 = 0 + 5b
3a = 0 + 5b
Remove the zero:
3a = 5b

Divide each side by '3'.
a = 1.666666667b

Simplifying
a = 1.666666667b
Solution
a = {-1.666666667b, 1.666666667b}

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