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Simplifying (x + -1) = (x + -3)(x + -4) Reorder the terms: (-1 + x) = (x + -3)(x + -4) Remove parenthesis around (-1 + x) -1 + x = (x + -3)(x + -4) Reorder the terms: -1 + x = (-3 + x)(x + -4) Reorder the terms: -1 + x = (-3 + x)(-4 + x) Multiply (-3 + x) * (-4 + x) -1 + x = (-3(-4 + x) + x(-4 + x)) -1 + x = ((-4 * -3 + x * -3) + x(-4 + x)) -1 + x = ((12 + -3x) + x(-4 + x)) -1 + x = (12 + -3x + (-4 * x + x * x)) -1 + x = (12 + -3x + (-4x + x2)) Combine like terms: -3x + -4x = -7x -1 + x = (12 + -7x + x2) Solving -1 + x = 12 + -7x + x2 Solving for variable 'x'. Reorder the terms: -1 + -12 + x + 7x + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2 Combine like terms: -1 + -12 = -13 -13 + x + 7x + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2 Combine like terms: x + 7x = 8x -13 + 8x + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2 Reorder the terms: -13 + 8x + -1x2 = 12 + -12 + -7x + 7x + x2 + -1x2 Combine like terms: 12 + -12 = 0 -13 + 8x + -1x2 = 0 + -7x + 7x + x2 + -1x2 -13 + 8x + -1x2 = -7x + 7x + x2 + -1x2 Combine like terms: -7x + 7x = 0 -13 + 8x + -1x2 = 0 + x2 + -1x2 -13 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -13 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 13 + -8x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -8x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8x + x2 = 0 + -13 -8x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8x + x2 = -13 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -13 + 16 Reorder the terms: 16 + -8x + x2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8x + x2 = 3 Factor a perfect square on the left side: (x + -4)(x + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -4 = 1.732050808 Simplifying x + -4 = 1.732050808 Reorder the terms: -4 + x = 1.732050808 Solving -4 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.732050808 + 4 x = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 x = 5.732050808 Simplifying x = 5.732050808Subproblem 2
x + -4 = -1.732050808 Simplifying x + -4 = -1.732050808 Reorder the terms: -4 + x = -1.732050808 Solving -4 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.732050808 + 4 x = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 x = 2.267949192 Simplifying x = 2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.732050808, 2.267949192}
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