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Simplifying 2x2 + x + -3 = -3x + -1 Reorder the terms: -3 + x + 2x2 = -3x + -1 Reorder the terms: -3 + x + 2x2 = -1 + -3x Solving -3 + x + 2x2 = -1 + -3x Solving for variable 'x'. Reorder the terms: -3 + 1 + x + 3x + 2x2 = -1 + -3x + 1 + 3x Combine like terms: -3 + 1 = -2 -2 + x + 3x + 2x2 = -1 + -3x + 1 + 3x Combine like terms: x + 3x = 4x -2 + 4x + 2x2 = -1 + -3x + 1 + 3x Reorder the terms: -2 + 4x + 2x2 = -1 + 1 + -3x + 3x Combine like terms: -1 + 1 = 0 -2 + 4x + 2x2 = 0 + -3x + 3x -2 + 4x + 2x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -2 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2x + x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + x2 = 0 Solving -1 + 2x + x2 = 0 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}Solution
x = {0.414213562, -2.414213562}
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