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Simplifying x(a + -1b) + -1x(a + b) + 4b2 = 0 (a * x + -1b * x) + -1x(a + b) + 4b2 = 0 (ax + -1bx) + -1x(a + b) + 4b2 = 0 ax + -1bx + (a * -1x + b * -1x) + 4b2 = 0 ax + -1bx + (-1ax + -1bx) + 4b2 = 0 Reorder the terms: ax + -1ax + -1bx + -1bx + 4b2 = 0 Combine like terms: ax + -1ax = 0 0 + -1bx + -1bx + 4b2 = 0 -1bx + -1bx + 4b2 = 0 Combine like terms: -1bx + -1bx = -2bx -2bx + 4b2 = 0 Solving -2bx + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2b'. 2b(-1x + 2b) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(-1x + 2b)' equal to zero and attempt to solve: Simplifying -1x + 2b = 0 Reorder the terms: 2b + -1x = 0 Solving 2b + -1x = 0 Move all terms containing b to the left, all other terms to the right. Add 'x' to each side of the equation. 2b + -1x + x = 0 + x Combine like terms: -1x + x = 0 2b + 0 = 0 + x 2b = 0 + x Remove the zero: 2b = x Divide each side by '2'. b = 0.5x Simplifying b = 0.5xSolution
b = {0, 0.5x}
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