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Simplifying 8x + 4 = 4x(2x + 1) Reorder the terms: 4 + 8x = 4x(2x + 1) Reorder the terms: 4 + 8x = 4x(1 + 2x) 4 + 8x = (1 * 4x + 2x * 4x) 4 + 8x = (4x + 8x2) Solving 4 + 8x = 4x + 8x2 Solving for variable 'x'. Combine like terms: 8x + -4x = 4x 4 + 4x + -8x2 = 4x + 8x2 + -4x + -8x2 Reorder the terms: 4 + 4x + -8x2 = 4x + -4x + 8x2 + -8x2 Combine like terms: 4x + -4x = 0 4 + 4x + -8x2 = 0 + 8x2 + -8x2 4 + 4x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 4 + 4x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + x + -2x2) = 0 Factor a trinomial. 4((1 + -1x)(1 + 2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-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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