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Simplifying 8ax + -7a2 = 19a + -5ax Solving 8ax + -7a2 = 19a + -5ax Solving for variable 'a'. Reorder the terms: -19a + 8ax + 5ax + -7a2 = 19a + -5ax + -19a + 5ax Combine like terms: 8ax + 5ax = 13ax -19a + 13ax + -7a2 = 19a + -5ax + -19a + 5ax Reorder the terms: -19a + 13ax + -7a2 = 19a + -19a + -5ax + 5ax Combine like terms: 19a + -19a = 0 -19a + 13ax + -7a2 = 0 + -5ax + 5ax -19a + 13ax + -7a2 = -5ax + 5ax Combine like terms: -5ax + 5ax = 0 -19a + 13ax + -7a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-19 + 13x + -7a) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-19 + 13x + -7a)' equal to zero and attempt to solve: Simplifying -19 + 13x + -7a = 0 Reorder the terms: -19 + -7a + 13x = 0 Solving -19 + -7a + 13x = 0 Move all terms containing a to the left, all other terms to the right. Add '19' to each side of the equation. -19 + -7a + 19 + 13x = 0 + 19 Reorder the terms: -19 + 19 + -7a + 13x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -7a + 13x = 0 + 19 -7a + 13x = 0 + 19 Combine like terms: 0 + 19 = 19 -7a + 13x = 19 Add '-13x' to each side of the equation. -7a + 13x + -13x = 19 + -13x Combine like terms: 13x + -13x = 0 -7a + 0 = 19 + -13x -7a = 19 + -13x Divide each side by '-7'. a = -2.714285714 + 1.857142857x Simplifying a = -2.714285714 + 1.857142857xSolution
a = {0, -2.714285714 + 1.857142857x}
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