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Simplifying 4x2 + -2x + k = (2x + -1a)(2x + -1a) Reorder the terms: k + -2x + 4x2 = (2x + -1a)(2x + -1a) Reorder the terms: k + -2x + 4x2 = (-1a + 2x)(2x + -1a) Reorder the terms: k + -2x + 4x2 = (-1a + 2x)(-1a + 2x) Multiply (-1a + 2x) * (-1a + 2x) k + -2x + 4x2 = (-1a * (-1a + 2x) + 2x * (-1a + 2x)) k + -2x + 4x2 = ((-1a * -1a + 2x * -1a) + 2x * (-1a + 2x)) Reorder the terms: k + -2x + 4x2 = ((-2ax + 1a2) + 2x * (-1a + 2x)) k + -2x + 4x2 = ((-2ax + 1a2) + 2x * (-1a + 2x)) k + -2x + 4x2 = (-2ax + 1a2 + (-1a * 2x + 2x * 2x)) k + -2x + 4x2 = (-2ax + 1a2 + (-2ax + 4x2)) Reorder the terms: k + -2x + 4x2 = (-2ax + -2ax + 1a2 + 4x2) Combine like terms: -2ax + -2ax = -4ax k + -2x + 4x2 = (-4ax + 1a2 + 4x2) Add '-4x2' to each side of the equation. k + -2x + 4x2 + -4x2 = -4ax + 1a2 + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 k + -2x + 0 = -4ax + 1a2 + 4x2 + -4x2 k + -2x = -4ax + 1a2 + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 k + -2x = -4ax + 1a2 + 0 k + -2x = -4ax + 1a2 Solving k + -2x = -4ax + 1a2 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2x' to each side of the equation. k + -2x + 2x = -4ax + 1a2 + 2x Combine like terms: -2x + 2x = 0 k + 0 = -4ax + 1a2 + 2x k = -4ax + 1a2 + 2x Simplifying k = -4ax + 1a2 + 2x
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