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Simplifying 0 = (4x2 + 1) + -1(6x2 + x + 1) Reorder the terms: 0 = (1 + 4x2) + -1(6x2 + x + 1) Remove parenthesis around (1 + 4x2) 0 = 1 + 4x2 + -1(6x2 + x + 1) Reorder the terms: 0 = 1 + 4x2 + -1(1 + x + 6x2) 0 = 1 + 4x2 + (1 * -1 + x * -1 + 6x2 * -1) 0 = 1 + 4x2 + (-1 + -1x + -6x2) Reorder the terms: 0 = 1 + -1 + -1x + 4x2 + -6x2 Combine like terms: 1 + -1 = 0 0 = 0 + -1x + 4x2 + -6x2 0 = -1x + 4x2 + -6x2 Combine like terms: 4x2 + -6x2 = -2x2 0 = -1x + -2x2 Solving 0 = -1x + -2x2 Solving for variable 'x'. Remove the zero: x + 2x2 = -1x + -2x2 + x + 2x2 Reorder the terms: x + 2x2 = -1x + x + -2x2 + 2x2 Combine like terms: -1x + x = 0 x + 2x2 = 0 + -2x2 + 2x2 x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {0, -0.5}
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