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Simplifying (x + -3)(x + -1) = 14 Reorder the terms: (-3 + x)(x + -1) = 14 Reorder the terms: (-3 + x)(-1 + x) = 14 Multiply (-3 + x) * (-1 + x) (-3(-1 + x) + x(-1 + x)) = 14 ((-1 * -3 + x * -3) + x(-1 + x)) = 14 ((3 + -3x) + x(-1 + x)) = 14 (3 + -3x + (-1 * x + x * x)) = 14 (3 + -3x + (-1x + x2)) = 14 Combine like terms: -3x + -1x = -4x (3 + -4x + x2) = 14 Solving 3 + -4x + x2 = 14 Solving for variable 'x'. Reorder the terms: 3 + -14 + -4x + x2 = 14 + -14 Combine like terms: 3 + -14 = -11 -11 + -4x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -11 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -4x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -4x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4x + x2 = 0 + 11 -4x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -4x + x2 = 11 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 11 + 4 Reorder the terms: 4 + -4x + x2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + -4x + x2 = 15 Factor a perfect square on the left side: (x + -2)(x + -2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -2) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -2 = 3.872983346 Simplifying x + -2 = 3.872983346 Reorder the terms: -2 + x = 3.872983346 Solving -2 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.872983346 + 2 x = 3.872983346 + 2 Combine like terms: 3.872983346 + 2 = 5.872983346 x = 5.872983346 Simplifying x = 5.872983346Subproblem 2
x + -2 = -3.872983346 Simplifying x + -2 = -3.872983346 Reorder the terms: -2 + x = -3.872983346 Solving -2 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.872983346 + 2 x = -3.872983346 + 2 Combine like terms: -3.872983346 + 2 = -1.872983346 x = -1.872983346 Simplifying x = -1.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.872983346, -1.872983346}
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