56a^2-14ab-7b^2=0

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Solution for 56a^2-14ab-7b^2=0 equation:


Simplifying
56a2 + -14ab + -7b2 = 0

Reorder the terms:
-14ab + 56a2 + -7b2 = 0

Solving
-14ab + 56a2 + -7b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-2ab + 8a2 + -1b2) = 0

Factor a trinomial.
7((2a + -1b)(4a + b)) = 0

Ignore the factor 7.

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 '(4a + b)' equal to zero and attempt to solve: Simplifying 4a + b = 0 Solving 4a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 4a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 4a + 0 = 0 + -1b 4a = 0 + -1b Remove the zero: 4a = -1b Divide each side by '4'. a = -0.25b Simplifying a = -0.25b

Solution

a = {0.5b, -0.25b}

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