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Simplifying a(a + -8b) + -8a(a + b) = 0 (a * a + -8b * a) + -8a(a + b) = 0 Reorder the terms: (-8ab + a2) + -8a(a + b) = 0 (-8ab + a2) + -8a(a + b) = 0 -8ab + a2 + (a * -8a + b * -8a) = 0 Reorder the terms: -8ab + a2 + (-8ab + -8a2) = 0 -8ab + a2 + (-8ab + -8a2) = 0 Reorder the terms: -8ab + -8ab + a2 + -8a2 = 0 Combine like terms: -8ab + -8ab = -16ab -16ab + a2 + -8a2 = 0 Combine like terms: a2 + -8a2 = -7a2 -16ab + -7a2 = 0 Solving -16ab + -7a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1a'. -1a(16b + 7a) = 0 Ignore the factor -1.Subproblem 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 '(16b + 7a)' equal to zero and attempt to solve: Simplifying 16b + 7a = 0 Reorder the terms: 7a + 16b = 0 Solving 7a + 16b = 0 Move all terms containing a to the left, all other terms to the right. Add '-16b' to each side of the equation. 7a + 16b + -16b = 0 + -16b Combine like terms: 16b + -16b = 0 7a + 0 = 0 + -16b 7a = 0 + -16b Remove the zero: 7a = -16b Divide each side by '7'. a = -2.285714286b Simplifying a = -2.285714286bSolution
a = {0, -2.285714286b}
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