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Simplifying x(1 + -2x) = 3(2x + -17) + -2x * 2x (1 * x + -2x * x) = 3(2x + -17) + -2x * 2x (1x + -2x2) = 3(2x + -17) + -2x * 2x Reorder the terms: 1x + -2x2 = 3(-17 + 2x) + -2x * 2x 1x + -2x2 = (-17 * 3 + 2x * 3) + -2x * 2x 1x + -2x2 = (-51 + 6x) + -2x * 2x Reorder the terms for easier multiplication: 1x + -2x2 = -51 + 6x + -2 * 2x * x Multiply -2 * 2 1x + -2x2 = -51 + 6x + -4x * x Multiply x * x 1x + -2x2 = -51 + 6x + -4x2 Solving 1x + -2x2 = -51 + 6x + -4x2 Solving for variable 'x'. Reorder the terms: 51 + 1x + -6x + -2x2 + 4x2 = -51 + 6x + -4x2 + 51 + -6x + 4x2 Combine like terms: 1x + -6x = -5x 51 + -5x + -2x2 + 4x2 = -51 + 6x + -4x2 + 51 + -6x + 4x2 Combine like terms: -2x2 + 4x2 = 2x2 51 + -5x + 2x2 = -51 + 6x + -4x2 + 51 + -6x + 4x2 Reorder the terms: 51 + -5x + 2x2 = -51 + 51 + 6x + -6x + -4x2 + 4x2 Combine like terms: -51 + 51 = 0 51 + -5x + 2x2 = 0 + 6x + -6x + -4x2 + 4x2 51 + -5x + 2x2 = 6x + -6x + -4x2 + 4x2 Combine like terms: 6x + -6x = 0 51 + -5x + 2x2 = 0 + -4x2 + 4x2 51 + -5x + 2x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 51 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + -2.5x + -25.5 + x2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + -2.5x + x2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + -2.5x + x2 = 0 + -25.5 -2.5x + x2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 -2.5x + x2 = -25.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -25.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -25.5 + 1.5625 Combine like terms: -25.5 + 1.5625 = -23.9375 1.5625 + -2.5x + x2 = -23.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -23.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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