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Simplifying (x + -2)(x + -2) = 3 Reorder the terms: (-2 + x)(x + -2) = 3 Reorder the terms: (-2 + x)(-2 + x) = 3 Multiply (-2 + x) * (-2 + x) (-2(-2 + x) + x(-2 + x)) = 3 ((-2 * -2 + x * -2) + x(-2 + x)) = 3 ((4 + -2x) + x(-2 + x)) = 3 (4 + -2x + (-2 * x + x * x)) = 3 (4 + -2x + (-2x + x2)) = 3 Combine like terms: -2x + -2x = -4x (4 + -4x + x2) = 3 Solving 4 + -4x + x2 = 3 Solving for variable 'x'. Reorder the terms: 4 + -3 + -4x + x2 = 3 + -3 Combine like terms: 4 + -3 = 1 1 + -4x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 1 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x + x2 = 0 + -1 -4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4x + x2 = -1 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 = -1 + 4 Reorder the terms: 4 + -4x + x2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4x + x2 = 3 Factor a perfect square on the left side: (x + -2)(x + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -2 = 1.732050808 Simplifying x + -2 = 1.732050808 Reorder the terms: -2 + x = 1.732050808 Solving -2 + x = 1.732050808 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 = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.732050808 + 2 x = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 x = 3.732050808 Simplifying x = 3.732050808Subproblem 2
x + -2 = -1.732050808 Simplifying x + -2 = -1.732050808 Reorder the terms: -2 + x = -1.732050808 Solving -2 + x = -1.732050808 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 = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.732050808 + 2 x = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 x = 0.267949192 Simplifying x = 0.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.732050808, 0.267949192}
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