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Simplifying x(a + b) + x(a + c) = 0 (a * x + b * x) + x(a + c) = 0 (ax + bx) + x(a + c) = 0 ax + bx + (a * x + c * x) = 0 ax + bx + (ax + cx) = 0 Reorder the terms: ax + ax + bx + cx = 0 Combine like terms: ax + ax = 2ax 2ax + bx + cx = 0 Solving 2ax + bx + cx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx' to each side of the equation. 2ax + bx + -1bx + cx = 0 + -1bx Combine like terms: bx + -1bx = 0 2ax + 0 + cx = 0 + -1bx 2ax + cx = 0 + -1bx Remove the zero: 2ax + cx = -1bx Add '-1cx' to each side of the equation. 2ax + cx + -1cx = -1bx + -1cx Combine like terms: cx + -1cx = 0 2ax + 0 = -1bx + -1cx 2ax = -1bx + -1cx Divide each side by '2x'. a = -0.5b + -0.5c Simplifying a = -0.5b + -0.5c
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