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Simplifying x2 + 2x + 0.9 = 0 Reorder the terms: 0.9 + 2x + x2 = 0 Solving 0.9 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + 2x + -0.9 + x2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + 2x + x2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + 2x + x2 = 0 + -0.9 2x + x2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 2x + x2 = -0.9 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 = -0.9 + 1 Reorder the terms: 1 + 2x + x2 = -0.9 + 1 Combine like terms: -0.9 + 1 = 0.1 1 + 2x + x2 = 0.1 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.1 Calculate the square root of the right side: 0.316227766 Break this problem into two subproblems by setting (x + 1) equal to 0.316227766 and -0.316227766.Subproblem 1
x + 1 = 0.316227766 Simplifying x + 1 = 0.316227766 Reorder the terms: 1 + x = 0.316227766 Solving 1 + x = 0.316227766 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 = 0.316227766 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.316227766 + -1 x = 0.316227766 + -1 Combine like terms: 0.316227766 + -1 = -0.683772234 x = -0.683772234 Simplifying x = -0.683772234Subproblem 2
x + 1 = -0.316227766 Simplifying x + 1 = -0.316227766 Reorder the terms: 1 + x = -0.316227766 Solving 1 + x = -0.316227766 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 = -0.316227766 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.316227766 + -1 x = -0.316227766 + -1 Combine like terms: -0.316227766 + -1 = -1.316227766 x = -1.316227766 Simplifying x = -1.316227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.683772234, -1.316227766}
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