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Simplifying (5x + -3)(1 + -4x) + x(3x + 7) = 8 Reorder the terms: (-3 + 5x)(1 + -4x) + x(3x + 7) = 8 Multiply (-3 + 5x) * (1 + -4x) (-3(1 + -4x) + 5x * (1 + -4x)) + x(3x + 7) = 8 ((1 * -3 + -4x * -3) + 5x * (1 + -4x)) + x(3x + 7) = 8 ((-3 + 12x) + 5x * (1 + -4x)) + x(3x + 7) = 8 (-3 + 12x + (1 * 5x + -4x * 5x)) + x(3x + 7) = 8 (-3 + 12x + (5x + -20x2)) + x(3x + 7) = 8 Combine like terms: 12x + 5x = 17x (-3 + 17x + -20x2) + x(3x + 7) = 8 Reorder the terms: -3 + 17x + -20x2 + x(7 + 3x) = 8 -3 + 17x + -20x2 + (7 * x + 3x * x) = 8 -3 + 17x + -20x2 + (7x + 3x2) = 8 Reorder the terms: -3 + 17x + 7x + -20x2 + 3x2 = 8 Combine like terms: 17x + 7x = 24x -3 + 24x + -20x2 + 3x2 = 8 Combine like terms: -20x2 + 3x2 = -17x2 -3 + 24x + -17x2 = 8 Solving -3 + 24x + -17x2 = 8 Solving for variable 'x'. Reorder the terms: -3 + -8 + 24x + -17x2 = 8 + -8 Combine like terms: -3 + -8 = -11 -11 + 24x + -17x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -11 + 24x + -17x2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. 0.6470588235 + -1.411764706x + x2 = 0 Move the constant term to the right: Add '-0.6470588235' to each side of the equation. 0.6470588235 + -1.411764706x + -0.6470588235 + x2 = 0 + -0.6470588235 Reorder the terms: 0.6470588235 + -0.6470588235 + -1.411764706x + x2 = 0 + -0.6470588235 Combine like terms: 0.6470588235 + -0.6470588235 = 0.0000000000 0.0000000000 + -1.411764706x + x2 = 0 + -0.6470588235 -1.411764706x + x2 = 0 + -0.6470588235 Combine like terms: 0 + -0.6470588235 = -0.6470588235 -1.411764706x + x2 = -0.6470588235 The x term is -1.411764706x. Take half its coefficient (-0.705882353). Square it (0.4982698963) and add it to both sides. Add '0.4982698963' to each side of the equation. -1.411764706x + 0.4982698963 + x2 = -0.6470588235 + 0.4982698963 Reorder the terms: 0.4982698963 + -1.411764706x + x2 = -0.6470588235 + 0.4982698963 Combine like terms: -0.6470588235 + 0.4982698963 = -0.1487889272 0.4982698963 + -1.411764706x + x2 = -0.1487889272 Factor a perfect square on the left side: (x + -0.705882353)(x + -0.705882353) = -0.1487889272 Can't calculate square root of the right side. The solution to this equation could not be determined.
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