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Simplifying (x + -1)(x + -2) = 4 Reorder the terms: (-1 + x)(x + -2) = 4 Reorder the terms: (-1 + x)(-2 + x) = 4 Multiply (-1 + x) * (-2 + x) (-1(-2 + x) + x(-2 + x)) = 4 ((-2 * -1 + x * -1) + x(-2 + x)) = 4 ((2 + -1x) + x(-2 + x)) = 4 (2 + -1x + (-2 * x + x * x)) = 4 (2 + -1x + (-2x + x2)) = 4 Combine like terms: -1x + -2x = -3x (2 + -3x + x2) = 4 Solving 2 + -3x + x2 = 4 Solving for variable 'x'. Reorder the terms: 2 + -4 + -3x + x2 = 4 + -4 Combine like terms: 2 + -4 = -2 -2 + -3x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -2 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -3x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x + x2 = 0 + 2 -3x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3x + x2 = 2 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + -3x + x2 = 4.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -1.5 = 2.061552813 Simplifying x + -1.5 = 2.061552813 Reorder the terms: -1.5 + x = 2.061552813 Solving -1.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.061552813 + 1.5 x = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 x = 3.561552813 Simplifying x = 3.561552813Subproblem 2
x + -1.5 = -2.061552813 Simplifying x + -1.5 = -2.061552813 Reorder the terms: -1.5 + x = -2.061552813 Solving -1.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.061552813 + 1.5 x = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 x = -0.561552813 Simplifying x = -0.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.561552813, -0.561552813}
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