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Simplifying 3x + 5x(2x + -1) = 8 + -3x(4 + -5x) Reorder the terms: 3x + 5x(-1 + 2x) = 8 + -3x(4 + -5x) 3x + (-1 * 5x + 2x * 5x) = 8 + -3x(4 + -5x) 3x + (-5x + 10x2) = 8 + -3x(4 + -5x) Combine like terms: 3x + -5x = -2x -2x + 10x2 = 8 + -3x(4 + -5x) -2x + 10x2 = 8 + (4 * -3x + -5x * -3x) -2x + 10x2 = 8 + (-12x + 15x2) Solving -2x + 10x2 = 8 + -12x + 15x2 Solving for variable 'x'. Reorder the terms: -8 + -2x + 12x + 10x2 + -15x2 = 8 + -12x + 15x2 + -8 + 12x + -15x2 Combine like terms: -2x + 12x = 10x -8 + 10x + 10x2 + -15x2 = 8 + -12x + 15x2 + -8 + 12x + -15x2 Combine like terms: 10x2 + -15x2 = -5x2 -8 + 10x + -5x2 = 8 + -12x + 15x2 + -8 + 12x + -15x2 Reorder the terms: -8 + 10x + -5x2 = 8 + -8 + -12x + 12x + 15x2 + -15x2 Combine like terms: 8 + -8 = 0 -8 + 10x + -5x2 = 0 + -12x + 12x + 15x2 + -15x2 -8 + 10x + -5x2 = -12x + 12x + 15x2 + -15x2 Combine like terms: -12x + 12x = 0 -8 + 10x + -5x2 = 0 + 15x2 + -15x2 -8 + 10x + -5x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -8 + 10x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.6 + -2x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -2x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -2x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -2x + x2 = 0 + -1.6 -2x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -2x + x2 = -1.6 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -1.6 + 1 Reorder the terms: 1 + -2x + x2 = -1.6 + 1 Combine like terms: -1.6 + 1 = -0.6 1 + -2x + x2 = -0.6 Factor a perfect square on the left side: (x + -1)(x + -1) = -0.6 Can't calculate square root of the right side. The solution to this equation could not be determined.
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