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Simplifying x2 + -0.4285 + -4x = 0 Reorder the terms: -0.4285 + -4x + x2 = 0 Solving -0.4285 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.4285' to each side of the equation. -0.4285 + -4x + 0.4285 + x2 = 0 + 0.4285 Reorder the terms: -0.4285 + 0.4285 + -4x + x2 = 0 + 0.4285 Combine like terms: -0.4285 + 0.4285 = 0.0000 0.0000 + -4x + x2 = 0 + 0.4285 -4x + x2 = 0 + 0.4285 Combine like terms: 0 + 0.4285 = 0.4285 -4x + x2 = 0.4285 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 = 0.4285 + 4 Reorder the terms: 4 + -4x + x2 = 0.4285 + 4 Combine like terms: 0.4285 + 4 = 4.4285 4 + -4x + x2 = 4.4285 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.4285 Calculate the square root of the right side: 2.104400152 Break this problem into two subproblems by setting (x + -2) equal to 2.104400152 and -2.104400152.Subproblem 1
x + -2 = 2.104400152 Simplifying x + -2 = 2.104400152 Reorder the terms: -2 + x = 2.104400152 Solving -2 + x = 2.104400152 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 = 2.104400152 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.104400152 + 2 x = 2.104400152 + 2 Combine like terms: 2.104400152 + 2 = 4.104400152 x = 4.104400152 Simplifying x = 4.104400152Subproblem 2
x + -2 = -2.104400152 Simplifying x + -2 = -2.104400152 Reorder the terms: -2 + x = -2.104400152 Solving -2 + x = -2.104400152 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 = -2.104400152 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.104400152 + 2 x = -2.104400152 + 2 Combine like terms: -2.104400152 + 2 = -0.104400152 x = -0.104400152 Simplifying x = -0.104400152Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.104400152, -0.104400152}
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