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Simplifying 3x(x + 3) + -1(x + -1) = (x + 5)(x + -2) Reorder the terms: 3x(3 + x) + -1(x + -1) = (x + 5)(x + -2) (3 * 3x + x * 3x) + -1(x + -1) = (x + 5)(x + -2) (9x + 3x2) + -1(x + -1) = (x + 5)(x + -2) Reorder the terms: 9x + 3x2 + -1(-1 + x) = (x + 5)(x + -2) 9x + 3x2 + (-1 * -1 + x * -1) = (x + 5)(x + -2) 9x + 3x2 + (1 + -1x) = (x + 5)(x + -2) Reorder the terms: 1 + 9x + -1x + 3x2 = (x + 5)(x + -2) Combine like terms: 9x + -1x = 8x 1 + 8x + 3x2 = (x + 5)(x + -2) Reorder the terms: 1 + 8x + 3x2 = (5 + x)(x + -2) Reorder the terms: 1 + 8x + 3x2 = (5 + x)(-2 + x) Multiply (5 + x) * (-2 + x) 1 + 8x + 3x2 = (5(-2 + x) + x(-2 + x)) 1 + 8x + 3x2 = ((-2 * 5 + x * 5) + x(-2 + x)) 1 + 8x + 3x2 = ((-10 + 5x) + x(-2 + x)) 1 + 8x + 3x2 = (-10 + 5x + (-2 * x + x * x)) 1 + 8x + 3x2 = (-10 + 5x + (-2x + x2)) Combine like terms: 5x + -2x = 3x 1 + 8x + 3x2 = (-10 + 3x + x2) Solving 1 + 8x + 3x2 = -10 + 3x + x2 Solving for variable 'x'. Reorder the terms: 1 + 10 + 8x + -3x + 3x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2 Combine like terms: 1 + 10 = 11 11 + 8x + -3x + 3x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2 Combine like terms: 8x + -3x = 5x 11 + 5x + 3x2 + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 11 + 5x + 2x2 = -10 + 3x + x2 + 10 + -3x + -1x2 Reorder the terms: 11 + 5x + 2x2 = -10 + 10 + 3x + -3x + x2 + -1x2 Combine like terms: -10 + 10 = 0 11 + 5x + 2x2 = 0 + 3x + -3x + x2 + -1x2 11 + 5x + 2x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 11 + 5x + 2x2 = 0 + x2 + -1x2 11 + 5x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 2.5x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 2.5x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 2.5x + x2 = 0 + -5.5 2.5x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 2.5x + x2 = -5.5 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 = -5.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -5.5 + 1.5625 Combine like terms: -5.5 + 1.5625 = -3.9375 1.5625 + 2.5x + x2 = -3.9375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -3.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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