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Simplifying x * x + -2x + -3.586 = 0 Multiply x * x x2 + -2x + -3.586 = 0 Reorder the terms: -3.586 + -2x + x2 = 0 Solving -3.586 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3.586' to each side of the equation. -3.586 + -2x + 3.586 + x2 = 0 + 3.586 Reorder the terms: -3.586 + 3.586 + -2x + x2 = 0 + 3.586 Combine like terms: -3.586 + 3.586 = 0.000 0.000 + -2x + x2 = 0 + 3.586 -2x + x2 = 0 + 3.586 Combine like terms: 0 + 3.586 = 3.586 -2x + x2 = 3.586 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 = 3.586 + 1 Reorder the terms: 1 + -2x + x2 = 3.586 + 1 Combine like terms: 3.586 + 1 = 4.586 1 + -2x + x2 = 4.586 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.586 Calculate the square root of the right side: 2.141494805 Break this problem into two subproblems by setting (x + -1) equal to 2.141494805 and -2.141494805.Subproblem 1
x + -1 = 2.141494805 Simplifying x + -1 = 2.141494805 Reorder the terms: -1 + x = 2.141494805 Solving -1 + x = 2.141494805 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 = 2.141494805 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.141494805 + 1 x = 2.141494805 + 1 Combine like terms: 2.141494805 + 1 = 3.141494805 x = 3.141494805 Simplifying x = 3.141494805Subproblem 2
x + -1 = -2.141494805 Simplifying x + -1 = -2.141494805 Reorder the terms: -1 + x = -2.141494805 Solving -1 + x = -2.141494805 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 = -2.141494805 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.141494805 + 1 x = -2.141494805 + 1 Combine like terms: -2.141494805 + 1 = -1.141494805 x = -1.141494805 Simplifying x = -1.141494805Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.141494805, -1.141494805}
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