25a^4-10a^2b^2+b^4=0

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Solution for 25a^4-10a^2b^2+b^4=0 equation:


Simplifying
25a4 + -10a2b2 + b4 = 0

Reorder the terms:
-10a2b2 + 25a4 + b4 = 0

Solving
-10a2b2 + 25a4 + b4 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a2 + -1b2)(5a2 + -1b2) = 0

Subproblem 1

Set the factor '(5a2 + -1b2)' equal to zero and attempt to solve: Simplifying 5a2 + -1b2 = 0 Solving 5a2 + -1b2 = 0 Move all terms containing a to the left, all other terms to the right. Add 'b2' to each side of the equation. 5a2 + -1b2 + b2 = 0 + b2 Combine like terms: -1b2 + b2 = 0 5a2 + 0 = 0 + b2 5a2 = 0 + b2 Remove the zero: 5a2 = b2 Divide each side by '5'. a2 = 0.2b2 Simplifying a2 = 0.2b2 Take the square root of each side: a = {-0.447213596b, 0.447213596b}

Subproblem 2

Set the factor '(5a2 + -1b2)' equal to zero and attempt to solve: Simplifying 5a2 + -1b2 = 0 Solving 5a2 + -1b2 = 0 Move all terms containing a to the left, all other terms to the right. Add 'b2' to each side of the equation. 5a2 + -1b2 + b2 = 0 + b2 Combine like terms: -1b2 + b2 = 0 5a2 + 0 = 0 + b2 5a2 = 0 + b2 Remove the zero: 5a2 = b2 Divide each side by '5'. a2 = 0.2b2 Simplifying a2 = 0.2b2 Take the square root of each side: a = {-0.447213596b, 0.447213596b}

Solution

a = {-0.447213596b, 0.447213596b, -0.447213596b, 0.447213596b}

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