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Simplifying 16x2 + 8x + -1(x + 4)(4x + 1) = 16x2 + 8x Reorder the terms: 16x2 + 8x + -1(4 + x)(4x + 1) = 16x2 + 8x Reorder the terms: 16x2 + 8x + -1(4 + x)(1 + 4x) = 16x2 + 8x Multiply (4 + x) * (1 + 4x) 16x2 + 8x + -1(4(1 + 4x) + x(1 + 4x)) = 16x2 + 8x 16x2 + 8x + -1((1 * 4 + 4x * 4) + x(1 + 4x)) = 16x2 + 8x 16x2 + 8x + -1((4 + 16x) + x(1 + 4x)) = 16x2 + 8x 16x2 + 8x + -1(4 + 16x + (1 * x + 4x * x)) = 16x2 + 8x 16x2 + 8x + -1(4 + 16x + (1x + 4x2)) = 16x2 + 8x Combine like terms: 16x + 1x = 17x 16x2 + 8x + -1(4 + 17x + 4x2) = 16x2 + 8x 16x2 + 8x + (4 * -1 + 17x * -1 + 4x2 * -1) = 16x2 + 8x 16x2 + 8x + (-4 + -17x + -4x2) = 16x2 + 8x Reorder the terms: -4 + 8x + -17x + 16x2 + -4x2 = 16x2 + 8x Combine like terms: 8x + -17x = -9x -4 + -9x + 16x2 + -4x2 = 16x2 + 8x Combine like terms: 16x2 + -4x2 = 12x2 -4 + -9x + 12x2 = 16x2 + 8x Reorder the terms: -4 + -9x + 12x2 = 8x + 16x2 Solving -4 + -9x + 12x2 = 8x + 16x2 Solving for variable 'x'. Reorder the terms: -4 + -9x + -8x + 12x2 + -16x2 = 8x + 16x2 + -8x + -16x2 Combine like terms: -9x + -8x = -17x -4 + -17x + 12x2 + -16x2 = 8x + 16x2 + -8x + -16x2 Combine like terms: 12x2 + -16x2 = -4x2 -4 + -17x + -4x2 = 8x + 16x2 + -8x + -16x2 Reorder the terms: -4 + -17x + -4x2 = 8x + -8x + 16x2 + -16x2 Combine like terms: 8x + -8x = 0 -4 + -17x + -4x2 = 0 + 16x2 + -16x2 -4 + -17x + -4x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -4 + -17x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 17x + 4x2) = 0 Factor a trinomial. -1((4 + x)(1 + 4x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {-4, -0.25}
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