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Simplifying 13 + -6x = (2x + -5)(2x + -5) + 3 Reorder the terms: 13 + -6x = (-5 + 2x)(2x + -5) + 3 Reorder the terms: 13 + -6x = (-5 + 2x)(-5 + 2x) + 3 Multiply (-5 + 2x) * (-5 + 2x) 13 + -6x = (-5(-5 + 2x) + 2x * (-5 + 2x)) + 3 13 + -6x = ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + 3 13 + -6x = ((25 + -10x) + 2x * (-5 + 2x)) + 3 13 + -6x = (25 + -10x + (-5 * 2x + 2x * 2x)) + 3 13 + -6x = (25 + -10x + (-10x + 4x2)) + 3 Combine like terms: -10x + -10x = -20x 13 + -6x = (25 + -20x + 4x2) + 3 Reorder the terms: 13 + -6x = 25 + 3 + -20x + 4x2 Combine like terms: 25 + 3 = 28 13 + -6x = 28 + -20x + 4x2 Solving 13 + -6x = 28 + -20x + 4x2 Solving for variable 'x'. Reorder the terms: 13 + -28 + -6x + 20x + -4x2 = 28 + -20x + 4x2 + -28 + 20x + -4x2 Combine like terms: 13 + -28 = -15 -15 + -6x + 20x + -4x2 = 28 + -20x + 4x2 + -28 + 20x + -4x2 Combine like terms: -6x + 20x = 14x -15 + 14x + -4x2 = 28 + -20x + 4x2 + -28 + 20x + -4x2 Reorder the terms: -15 + 14x + -4x2 = 28 + -28 + -20x + 20x + 4x2 + -4x2 Combine like terms: 28 + -28 = 0 -15 + 14x + -4x2 = 0 + -20x + 20x + 4x2 + -4x2 -15 + 14x + -4x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 -15 + 14x + -4x2 = 0 + 4x2 + -4x2 -15 + 14x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + 14x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.75 + -3.5x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -3.5x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -3.5x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -3.5x + x2 = 0 + -3.75 -3.5x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -3.5x + x2 = -3.75 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -3.75 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -3.75 + 3.0625 Combine like terms: -3.75 + 3.0625 = -0.6875 3.0625 + -3.5x + x2 = -0.6875 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -0.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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