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Simplifying x(x + -2) + x(x + 1) = x + -2(x) + x + -2(x + 5) Reorder the terms: x(-2 + x) + x(x + 1) = x + -2(x) + x + -2(x + 5) (-2 * x + x * x) + x(x + 1) = x + -2(x) + x + -2(x + 5) (-2x + x2) + x(x + 1) = x + -2(x) + x + -2(x + 5) Reorder the terms: -2x + x2 + x(1 + x) = x + -2(x) + x + -2(x + 5) -2x + x2 + (1 * x + x * x) = x + -2(x) + x + -2(x + 5) -2x + x2 + (1x + x2) = x + -2(x) + x + -2(x + 5) Reorder the terms: -2x + 1x + x2 + x2 = x + -2(x) + x + -2(x + 5) Combine like terms: -2x + 1x = -1x -1x + x2 + x2 = x + -2(x) + x + -2(x + 5) Combine like terms: x2 + x2 = 2x2 -1x + 2x2 = x + -2(x) + x + -2(x + 5) Reorder the terms: -1x + 2x2 = x + -2x + x + -2(5 + x) -1x + 2x2 = x + -2x + x + (5 * -2 + x * -2) -1x + 2x2 = x + -2x + x + (-10 + -2x) Reorder the terms: -1x + 2x2 = -10 + x + -2x + x + -2x Combine like terms: x + -2x = -1x -1x + 2x2 = -10 + -1x + x + -2x Combine like terms: -1x + x = 0 -1x + 2x2 = -10 + 0 + -2x -1x + 2x2 = -10 + -2x Solving -1x + 2x2 = -10 + -2x Solving for variable 'x'. Reorder the terms: 10 + -1x + 2x + 2x2 = -10 + -2x + 10 + 2x Combine like terms: -1x + 2x = 1x 10 + 1x + 2x2 = -10 + -2x + 10 + 2x Reorder the terms: 10 + 1x + 2x2 = -10 + 10 + -2x + 2x Combine like terms: -10 + 10 = 0 10 + 1x + 2x2 = 0 + -2x + 2x 10 + 1x + 2x2 = -2x + 2x Combine like terms: -2x + 2x = 0 10 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 0.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 0.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 0.5x + x2 = 0 + -5 0.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 0.5x + x2 = -5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -5 + 0.0625 Combine like terms: -5 + 0.0625 = -4.9375 0.0625 + 0.5x + x2 = -4.9375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -4.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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