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Simplifying (2x + -4)(2x + -4) = 8 Reorder the terms: (-4 + 2x)(2x + -4) = 8 Reorder the terms: (-4 + 2x)(-4 + 2x) = 8 Multiply (-4 + 2x) * (-4 + 2x) (-4(-4 + 2x) + 2x * (-4 + 2x)) = 8 ((-4 * -4 + 2x * -4) + 2x * (-4 + 2x)) = 8 ((16 + -8x) + 2x * (-4 + 2x)) = 8 (16 + -8x + (-4 * 2x + 2x * 2x)) = 8 (16 + -8x + (-8x + 4x2)) = 8 Combine like terms: -8x + -8x = -16x (16 + -16x + 4x2) = 8 Solving 16 + -16x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: 16 + -8 + -16x + 4x2 = 8 + -8 Combine like terms: 16 + -8 = 8 8 + -16x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 8 + -16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -4x + x2)' equal to zero and attempt to solve: Simplifying 2 + -4x + x2 = 0 Solving 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}Solution
x = {3.414213562, 0.585786438}
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