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Simplifying (4x + 5)(x + -2) + (x + -5)(x + -5) = 0 Reorder the terms: (5 + 4x)(x + -2) + (x + -5)(x + -5) = 0 Reorder the terms: (5 + 4x)(-2 + x) + (x + -5)(x + -5) = 0 Multiply (5 + 4x) * (-2 + x) (5(-2 + x) + 4x * (-2 + x)) + (x + -5)(x + -5) = 0 ((-2 * 5 + x * 5) + 4x * (-2 + x)) + (x + -5)(x + -5) = 0 ((-10 + 5x) + 4x * (-2 + x)) + (x + -5)(x + -5) = 0 (-10 + 5x + (-2 * 4x + x * 4x)) + (x + -5)(x + -5) = 0 (-10 + 5x + (-8x + 4x2)) + (x + -5)(x + -5) = 0 Combine like terms: 5x + -8x = -3x (-10 + -3x + 4x2) + (x + -5)(x + -5) = 0 Reorder the terms: -10 + -3x + 4x2 + (-5 + x)(x + -5) = 0 Reorder the terms: -10 + -3x + 4x2 + (-5 + x)(-5 + x) = 0 Multiply (-5 + x) * (-5 + x) -10 + -3x + 4x2 + (-5(-5 + x) + x(-5 + x)) = 0 -10 + -3x + 4x2 + ((-5 * -5 + x * -5) + x(-5 + x)) = 0 -10 + -3x + 4x2 + ((25 + -5x) + x(-5 + x)) = 0 -10 + -3x + 4x2 + (25 + -5x + (-5 * x + x * x)) = 0 -10 + -3x + 4x2 + (25 + -5x + (-5x + x2)) = 0 Combine like terms: -5x + -5x = -10x -10 + -3x + 4x2 + (25 + -10x + x2) = 0 Reorder the terms: -10 + 25 + -3x + -10x + 4x2 + x2 = 0 Combine like terms: -10 + 25 = 15 15 + -3x + -10x + 4x2 + x2 = 0 Combine like terms: -3x + -10x = -13x 15 + -13x + 4x2 + x2 = 0 Combine like terms: 4x2 + x2 = 5x2 15 + -13x + 5x2 = 0 Solving 15 + -13x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + -2.6x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2.6x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -2.6x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2.6x + x2 = 0 + -3 -2.6x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2.6x + x2 = -3 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = -3 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = -3 + 1.69 Combine like terms: -3 + 1.69 = -1.31 1.69 + -2.6x + x2 = -1.31 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = -1.31 Can't calculate square root of the right side. The solution to this equation could not be determined.
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