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Simplifying (x + 4)(x + -3) + -1(8x + 3)(x + -1) = 0 Reorder the terms: (4 + x)(x + -3) + -1(8x + 3)(x + -1) = 0 Reorder the terms: (4 + x)(-3 + x) + -1(8x + 3)(x + -1) = 0 Multiply (4 + x) * (-3 + x) (4(-3 + x) + x(-3 + x)) + -1(8x + 3)(x + -1) = 0 ((-3 * 4 + x * 4) + x(-3 + x)) + -1(8x + 3)(x + -1) = 0 ((-12 + 4x) + x(-3 + x)) + -1(8x + 3)(x + -1) = 0 (-12 + 4x + (-3 * x + x * x)) + -1(8x + 3)(x + -1) = 0 (-12 + 4x + (-3x + x2)) + -1(8x + 3)(x + -1) = 0 Combine like terms: 4x + -3x = 1x (-12 + 1x + x2) + -1(8x + 3)(x + -1) = 0 Reorder the terms: -12 + 1x + x2 + -1(3 + 8x)(x + -1) = 0 Reorder the terms: -12 + 1x + x2 + -1(3 + 8x)(-1 + x) = 0 Multiply (3 + 8x) * (-1 + x) -12 + 1x + x2 + -1(3(-1 + x) + 8x * (-1 + x)) = 0 -12 + 1x + x2 + -1((-1 * 3 + x * 3) + 8x * (-1 + x)) = 0 -12 + 1x + x2 + -1((-3 + 3x) + 8x * (-1 + x)) = 0 -12 + 1x + x2 + -1(-3 + 3x + (-1 * 8x + x * 8x)) = 0 -12 + 1x + x2 + -1(-3 + 3x + (-8x + 8x2)) = 0 Combine like terms: 3x + -8x = -5x -12 + 1x + x2 + -1(-3 + -5x + 8x2) = 0 -12 + 1x + x2 + (-3 * -1 + -5x * -1 + 8x2 * -1) = 0 -12 + 1x + x2 + (3 + 5x + -8x2) = 0 Reorder the terms: -12 + 3 + 1x + 5x + x2 + -8x2 = 0 Combine like terms: -12 + 3 = -9 -9 + 1x + 5x + x2 + -8x2 = 0 Combine like terms: 1x + 5x = 6x -9 + 6x + x2 + -8x2 = 0 Combine like terms: x2 + -8x2 = -7x2 -9 + 6x + -7x2 = 0 Solving -9 + 6x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1.285714286 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -0.8571428571x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -0.8571428571x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + -1.285714286 -0.8571428571x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -0.8571428571x + x2 = -1.285714286 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = -1.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = -1.285714286 + 0.1836734694 Combine like terms: -1.285714286 + 0.1836734694 = -1.1020408166 0.1836734694 + -0.8571428571x + x2 = -1.1020408166 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = -1.1020408166 Can't calculate square root of the right side. The solution to this equation could not be determined.
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