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Simplifying 4x(x + -4) = (2x + 1)(x + -4) Reorder the terms: 4x(-4 + x) = (2x + 1)(x + -4) (-4 * 4x + x * 4x) = (2x + 1)(x + -4) (-16x + 4x2) = (2x + 1)(x + -4) Reorder the terms: -16x + 4x2 = (1 + 2x)(x + -4) Reorder the terms: -16x + 4x2 = (1 + 2x)(-4 + x) Multiply (1 + 2x) * (-4 + x) -16x + 4x2 = (1(-4 + x) + 2x * (-4 + x)) -16x + 4x2 = ((-4 * 1 + x * 1) + 2x * (-4 + x)) -16x + 4x2 = ((-4 + 1x) + 2x * (-4 + x)) -16x + 4x2 = (-4 + 1x + (-4 * 2x + x * 2x)) -16x + 4x2 = (-4 + 1x + (-8x + 2x2)) Combine like terms: 1x + -8x = -7x -16x + 4x2 = (-4 + -7x + 2x2) Solving -16x + 4x2 = -4 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: 4 + -16x + 7x + 4x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2 Combine like terms: -16x + 7x = -9x 4 + -9x + 4x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 4 + -9x + 2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2 Reorder the terms: 4 + -9x + 2x2 = -4 + 4 + -7x + 7x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 4 + -9x + 2x2 = 0 + -7x + 7x + 2x2 + -2x2 4 + -9x + 2x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 4 + -9x + 2x2 = 0 + 2x2 + -2x2 4 + -9x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4 + -9x + 2x2 = 0 Factor a trinomial. (1 + -2x)(4 + -1x) = 0Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0.5, 4}
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