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Simplifying (x + -2)(x + 1) = 3x + -4 Reorder the terms: (-2 + x)(x + 1) = 3x + -4 Reorder the terms: (-2 + x)(1 + x) = 3x + -4 Multiply (-2 + x) * (1 + x) (-2(1 + x) + x(1 + x)) = 3x + -4 ((1 * -2 + x * -2) + x(1 + x)) = 3x + -4 ((-2 + -2x) + x(1 + x)) = 3x + -4 (-2 + -2x + (1 * x + x * x)) = 3x + -4 (-2 + -2x + (1x + x2)) = 3x + -4 Combine like terms: -2x + 1x = -1x (-2 + -1x + x2) = 3x + -4 Reorder the terms: -2 + -1x + x2 = -4 + 3x Solving -2 + -1x + x2 = -4 + 3x Solving for variable 'x'. Reorder the terms: -2 + 4 + -1x + -3x + x2 = -4 + 3x + 4 + -3x Combine like terms: -2 + 4 = 2 2 + -1x + -3x + x2 = -4 + 3x + 4 + -3x Combine like terms: -1x + -3x = -4x 2 + -4x + x2 = -4 + 3x + 4 + -3x Reorder the terms: 2 + -4x + x2 = -4 + 4 + 3x + -3x Combine like terms: -4 + 4 = 0 2 + -4x + x2 = 0 + 3x + -3x 2 + -4x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 2 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4x + x2 = 0 + -2 -4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4x + x2 = -2 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 = -2 + 4 Reorder the terms: 4 + -4x + x2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4x + x2 = 2 Factor a perfect square on the left side: (x + -2)(x + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -2 = 1.414213562 Simplifying x + -2 = 1.414213562 Reorder the terms: -2 + x = 1.414213562 Solving -2 + x = 1.414213562 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 = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.414213562 + 2 x = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 x = 3.414213562 Simplifying x = 3.414213562Subproblem 2
x + -2 = -1.414213562 Simplifying x + -2 = -1.414213562 Reorder the terms: -2 + x = -1.414213562 Solving -2 + x = -1.414213562 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 = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.414213562 + 2 x = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 x = 0.585786438 Simplifying x = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.414213562, 0.585786438}
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