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Simplifying x2 + 2x = 0.19 Reorder the terms: 2x + x2 = 0.19 Solving 2x + x2 = 0.19 Solving for variable 'x'. Reorder the terms: -0.19 + 2x + x2 = 0.19 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 -0.19 + 2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.19' to each side of the equation. -0.19 + 2x + 0.19 + x2 = 0.00 + 0.19 Reorder the terms: -0.19 + 0.19 + 2x + x2 = 0.00 + 0.19 Combine like terms: -0.19 + 0.19 = 0.00 0.00 + 2x + x2 = 0.00 + 0.19 2x + x2 = 0.00 + 0.19 Combine like terms: 0.00 + 0.19 = 0.19 2x + x2 = 0.19 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 = 0.19 + 1 Reorder the terms: 1 + 2x + x2 = 0.19 + 1 Combine like terms: 0.19 + 1 = 1.19 1 + 2x + x2 = 1.19 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.19 Calculate the square root of the right side: 1.090871211 Break this problem into two subproblems by setting (x + 1) equal to 1.090871211 and -1.090871211.Subproblem 1
x + 1 = 1.090871211 Simplifying x + 1 = 1.090871211 Reorder the terms: 1 + x = 1.090871211 Solving 1 + x = 1.090871211 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 = 1.090871211 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.090871211 + -1 x = 1.090871211 + -1 Combine like terms: 1.090871211 + -1 = 0.090871211 x = 0.090871211 Simplifying x = 0.090871211Subproblem 2
x + 1 = -1.090871211 Simplifying x + 1 = -1.090871211 Reorder the terms: 1 + x = -1.090871211 Solving 1 + x = -1.090871211 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 = -1.090871211 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.090871211 + -1 x = -1.090871211 + -1 Combine like terms: -1.090871211 + -1 = -2.090871211 x = -2.090871211 Simplifying x = -2.090871211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.090871211, -2.090871211}
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