10a^2-3ab-b^2=0

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Solution for 10a^2-3ab-b^2=0 equation:


Simplifying
10a2 + -3ab + -1b2 = 0

Reorder the terms:
-3ab + 10a2 + -1b2 = 0

Solving
-3ab + 10a2 + -1b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -1b)(5a + b) = 0

Subproblem 1

Set the factor '(2a + -1b)' equal to zero and attempt to solve: Simplifying 2a + -1b = 0 Solving 2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5b

Subproblem 2

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

Solution

a = {0.5b, -0.2b}

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