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Simplifying 5x(x + 2) + -2(x + -1) + -3(x + -1)(x + 2) = 0 Reorder the terms: 5x(2 + x) + -2(x + -1) + -3(x + -1)(x + 2) = 0 (2 * 5x + x * 5x) + -2(x + -1) + -3(x + -1)(x + 2) = 0 (10x + 5x2) + -2(x + -1) + -3(x + -1)(x + 2) = 0 Reorder the terms: 10x + 5x2 + -2(-1 + x) + -3(x + -1)(x + 2) = 0 10x + 5x2 + (-1 * -2 + x * -2) + -3(x + -1)(x + 2) = 0 10x + 5x2 + (2 + -2x) + -3(x + -1)(x + 2) = 0 Reorder the terms: 10x + 5x2 + 2 + -2x + -3(-1 + x)(x + 2) = 0 Reorder the terms: 10x + 5x2 + 2 + -2x + -3(-1 + x)(2 + x) = 0 Multiply (-1 + x) * (2 + x) 10x + 5x2 + 2 + -2x + -3(-1(2 + x) + x(2 + x)) = 0 10x + 5x2 + 2 + -2x + -3((2 * -1 + x * -1) + x(2 + x)) = 0 10x + 5x2 + 2 + -2x + -3((-2 + -1x) + x(2 + x)) = 0 10x + 5x2 + 2 + -2x + -3(-2 + -1x + (2 * x + x * x)) = 0 10x + 5x2 + 2 + -2x + -3(-2 + -1x + (2x + x2)) = 0 Combine like terms: -1x + 2x = 1x 10x + 5x2 + 2 + -2x + -3(-2 + 1x + x2) = 0 10x + 5x2 + 2 + -2x + (-2 * -3 + 1x * -3 + x2 * -3) = 0 10x + 5x2 + 2 + -2x + (6 + -3x + -3x2) = 0 Reorder the terms: 2 + 6 + 10x + -2x + -3x + 5x2 + -3x2 = 0 Combine like terms: 2 + 6 = 8 8 + 10x + -2x + -3x + 5x2 + -3x2 = 0 Combine like terms: 10x + -2x = 8x 8 + 8x + -3x + 5x2 + -3x2 = 0 Combine like terms: 8x + -3x = 5x 8 + 5x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 8 + 5x + 2x2 = 0 Solving 8 + 5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 2.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 2.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.5x + x2 = 0 + -4 2.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.5x + x2 = -4 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 = -4 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -4 + 1.5625 Combine like terms: -4 + 1.5625 = -2.4375 1.5625 + 2.5x + x2 = -2.4375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -2.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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