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Simplifying 4x(2x + -1) = (x + 7)(x + -2) Reorder the terms: 4x(-1 + 2x) = (x + 7)(x + -2) (-1 * 4x + 2x * 4x) = (x + 7)(x + -2) (-4x + 8x2) = (x + 7)(x + -2) Reorder the terms: -4x + 8x2 = (7 + x)(x + -2) Reorder the terms: -4x + 8x2 = (7 + x)(-2 + x) Multiply (7 + x) * (-2 + x) -4x + 8x2 = (7(-2 + x) + x(-2 + x)) -4x + 8x2 = ((-2 * 7 + x * 7) + x(-2 + x)) -4x + 8x2 = ((-14 + 7x) + x(-2 + x)) -4x + 8x2 = (-14 + 7x + (-2 * x + x * x)) -4x + 8x2 = (-14 + 7x + (-2x + x2)) Combine like terms: 7x + -2x = 5x -4x + 8x2 = (-14 + 5x + x2) Solving -4x + 8x2 = -14 + 5x + x2 Solving for variable 'x'. Reorder the terms: 14 + -4x + -5x + 8x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2 Combine like terms: -4x + -5x = -9x 14 + -9x + 8x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2 Combine like terms: 8x2 + -1x2 = 7x2 14 + -9x + 7x2 = -14 + 5x + x2 + 14 + -5x + -1x2 Reorder the terms: 14 + -9x + 7x2 = -14 + 14 + 5x + -5x + x2 + -1x2 Combine like terms: -14 + 14 = 0 14 + -9x + 7x2 = 0 + 5x + -5x + x2 + -1x2 14 + -9x + 7x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 14 + -9x + 7x2 = 0 + x2 + -1x2 14 + -9x + 7x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 14 + -9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.285714286x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1.285714286x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.285714286x + x2 = 0 + -2 -1.285714286x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.285714286x + x2 = -2 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = -2 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = -2 + 0.4132653063 Combine like terms: -2 + 0.4132653063 = -1.5867346937 0.4132653063 + -1.285714286x + x2 = -1.5867346937 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = -1.5867346937 Can't calculate square root of the right side. The solution to this equation could not be determined.
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