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Simplifying x2 + -2x + -1.396 = 0 Reorder the terms: -1.396 + -2x + x2 = 0 Solving -1.396 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.396' to each side of the equation. -1.396 + -2x + 1.396 + x2 = 0 + 1.396 Reorder the terms: -1.396 + 1.396 + -2x + x2 = 0 + 1.396 Combine like terms: -1.396 + 1.396 = 0.000 0.000 + -2x + x2 = 0 + 1.396 -2x + x2 = 0 + 1.396 Combine like terms: 0 + 1.396 = 1.396 -2x + x2 = 1.396 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 = 1.396 + 1 Reorder the terms: 1 + -2x + x2 = 1.396 + 1 Combine like terms: 1.396 + 1 = 2.396 1 + -2x + x2 = 2.396 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.396 Calculate the square root of the right side: 1.547901806 Break this problem into two subproblems by setting (x + -1) equal to 1.547901806 and -1.547901806.Subproblem 1
x + -1 = 1.547901806 Simplifying x + -1 = 1.547901806 Reorder the terms: -1 + x = 1.547901806 Solving -1 + x = 1.547901806 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 = 1.547901806 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.547901806 + 1 x = 1.547901806 + 1 Combine like terms: 1.547901806 + 1 = 2.547901806 x = 2.547901806 Simplifying x = 2.547901806Subproblem 2
x + -1 = -1.547901806 Simplifying x + -1 = -1.547901806 Reorder the terms: -1 + x = -1.547901806 Solving -1 + x = -1.547901806 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 = -1.547901806 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.547901806 + 1 x = -1.547901806 + 1 Combine like terms: -1.547901806 + 1 = -0.547901806 x = -0.547901806 Simplifying x = -0.547901806Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.547901806, -0.547901806}
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