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Simplifying (4x2 + -2x + 1) + -1(3x2 + -4x + 2) = 0 Reorder the terms: (1 + -2x + 4x2) + -1(3x2 + -4x + 2) = 0 Remove parenthesis around (1 + -2x + 4x2) 1 + -2x + 4x2 + -1(3x2 + -4x + 2) = 0 Reorder the terms: 1 + -2x + 4x2 + -1(2 + -4x + 3x2) = 0 1 + -2x + 4x2 + (2 * -1 + -4x * -1 + 3x2 * -1) = 0 1 + -2x + 4x2 + (-2 + 4x + -3x2) = 0 Reorder the terms: 1 + -2 + -2x + 4x + 4x2 + -3x2 = 0 Combine like terms: 1 + -2 = -1 -1 + -2x + 4x + 4x2 + -3x2 = 0 Combine like terms: -2x + 4x = 2x -1 + 2x + 4x2 + -3x2 = 0 Combine like terms: 4x2 + -3x2 = 1x2 -1 + 2x + 1x2 = 0 Solving -1 + 2x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x + x2 = 0 + 1 2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2x + x2 = 1 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1 + 1 Reorder the terms: 1 + 2x + x2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2x + x2 = 2 Factor a perfect square on the left side: (x + 1)(x + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 1 = 1.414213562 Simplifying x + 1 = 1.414213562 Reorder the terms: 1 + x = 1.414213562 Solving 1 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.414213562 + -1 x = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 x = 0.414213562 Simplifying x = 0.414213562Subproblem 2
x + 1 = -1.414213562 Simplifying x + 1 = -1.414213562 Reorder the terms: 1 + x = -1.414213562 Solving 1 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.414213562 + -1 x = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 x = -2.414213562 Simplifying x = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.414213562, -2.414213562}
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