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Simplifying (7x + -1a)(x + -2a) = 0 Reorder the terms: (-1a + 7x)(x + -2a) = 0 Reorder the terms: (-1a + 7x)(-2a + x) = 0 Multiply (-1a + 7x) * (-2a + x) (-1a * (-2a + x) + 7x * (-2a + x)) = 0 ((-2a * -1a + x * -1a) + 7x * (-2a + x)) = 0 Reorder the terms: ((-1ax + 2a2) + 7x * (-2a + x)) = 0 ((-1ax + 2a2) + 7x * (-2a + x)) = 0 (-1ax + 2a2 + (-2a * 7x + x * 7x)) = 0 (-1ax + 2a2 + (-14ax + 7x2)) = 0 Reorder the terms: (-1ax + -14ax + 2a2 + 7x2) = 0 Combine like terms: -1ax + -14ax = -15ax (-15ax + 2a2 + 7x2) = 0 Solving -15ax + 2a2 + 7x2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -7x)(2a + -1x) = 0Subproblem 1
Set the factor '(a + -7x)' equal to zero and attempt to solve: Simplifying a + -7x = 0 Solving a + -7x = 0 Move all terms containing a to the left, all other terms to the right. Add '7x' to each side of the equation. a + -7x + 7x = 0 + 7x Combine like terms: -7x + 7x = 0 a + 0 = 0 + 7x a = 0 + 7x Remove the zero: a = 7x Simplifying a = 7xSubproblem 2
Set the factor '(2a + -1x)' equal to zero and attempt to solve: Simplifying 2a + -1x = 0 Solving 2a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. 2a + -1x + x = 0 + x Combine like terms: -1x + x = 0 2a + 0 = 0 + x 2a = 0 + x Remove the zero: 2a = x Divide each side by '2'. a = 0.5x Simplifying a = 0.5xSolution
a = {7x, 0.5x}
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