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Simplifying 2x(2x + 2) + (2x + 2) = 0 Reorder the terms: 2x(2 + 2x) + (2x + 2) = 0 (2 * 2x + 2x * 2x) + (2x + 2) = 0 (4x + 4x2) + (2x + 2) = 0 Reorder the terms: 4x + 4x2 + (2 + 2x) = 0 Remove parenthesis around (2 + 2x) 4x + 4x2 + 2 + 2x = 0 Reorder the terms: 2 + 4x + 2x + 4x2 = 0 Combine like terms: 4x + 2x = 6x 2 + 6x + 4x2 = 0 Solving 2 + 6x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 3x + 2x2) = 0 Factor a trinomial. 2((1 + x)(1 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 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 = {-1, -0.5}
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