a^2-9ab-52b^2=0

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Solution for a^2-9ab-52b^2=0 equation:


Simplifying
a2 + -9ab + -52b2 = 0

Reorder the terms:
-9ab + a2 + -52b2 = 0

Solving
-9ab + a2 + -52b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -13b)(a + 4b) = 0

Subproblem 1

Set the factor '(a + -13b)' equal to zero and attempt to solve: Simplifying a + -13b = 0 Solving a + -13b = 0 Move all terms containing a to the left, all other terms to the right. Add '13b' to each side of the equation. a + -13b + 13b = 0 + 13b Combine like terms: -13b + 13b = 0 a + 0 = 0 + 13b a = 0 + 13b Remove the zero: a = 13b Simplifying a = 13b

Subproblem 2

Set the factor '(a + 4b)' equal to zero and attempt to solve: Simplifying a + 4b = 0 Solving a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 a + 0 = 0 + -4b a = 0 + -4b Remove the zero: a = -4b Simplifying a = -4b

Solution

a = {13b, -4b}

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