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Simplifying x2 + 2x + 0.09 = 0 Reorder the terms: 0.09 + 2x + x2 = 0 Solving 0.09 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.09' to each side of the equation. 0.09 + 2x + -0.09 + x2 = 0 + -0.09 Reorder the terms: 0.09 + -0.09 + 2x + x2 = 0 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + 2x + x2 = 0 + -0.09 2x + x2 = 0 + -0.09 Combine like terms: 0 + -0.09 = -0.09 2x + x2 = -0.09 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 = -0.09 + 1 Reorder the terms: 1 + 2x + x2 = -0.09 + 1 Combine like terms: -0.09 + 1 = 0.91 1 + 2x + x2 = 0.91 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.91 Calculate the square root of the right side: 0.953939201 Break this problem into two subproblems by setting (x + 1) equal to 0.953939201 and -0.953939201.Subproblem 1
x + 1 = 0.953939201 Simplifying x + 1 = 0.953939201 Reorder the terms: 1 + x = 0.953939201 Solving 1 + x = 0.953939201 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 = 0.953939201 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.953939201 + -1 x = 0.953939201 + -1 Combine like terms: 0.953939201 + -1 = -0.046060799 x = -0.046060799 Simplifying x = -0.046060799Subproblem 2
x + 1 = -0.953939201 Simplifying x + 1 = -0.953939201 Reorder the terms: 1 + x = -0.953939201 Solving 1 + x = -0.953939201 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 = -0.953939201 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.953939201 + -1 x = -0.953939201 + -1 Combine like terms: -0.953939201 + -1 = -1.953939201 x = -1.953939201 Simplifying x = -1.953939201Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.046060799, -1.953939201}
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