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Simplifying 3x(1 + -4x) = 8 + -12x (1 * 3x + -4x * 3x) = 8 + -12x (3x + -12x2) = 8 + -12x Solving 3x + -12x2 = 8 + -12x Solving for variable 'x'. Reorder the terms: -8 + 3x + 12x + -12x2 = 8 + -12x + -8 + 12x Combine like terms: 3x + 12x = 15x -8 + 15x + -12x2 = 8 + -12x + -8 + 12x Reorder the terms: -8 + 15x + -12x2 = 8 + -8 + -12x + 12x Combine like terms: 8 + -8 = 0 -8 + 15x + -12x2 = 0 + -12x + 12x -8 + 15x + -12x2 = -12x + 12x Combine like terms: -12x + 12x = 0 -8 + 15x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 0.6666666667 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -1.25x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -1.25x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -1.25x + x2 = 0 + -0.6666666667 -1.25x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -1.25x + x2 = -0.6666666667 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.6666666667 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.6666666667 + 0.390625 Combine like terms: -0.6666666667 + 0.390625 = -0.2760416667 0.390625 + -1.25x + x2 = -0.2760416667 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -0.2760416667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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