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Simplifying 2x + (x2) = 2.1 2x + x2 = 2.1 Solving 2x + x2 = 2.1 Solving for variable 'x'. Reorder the terms: -2.1 + 2x + x2 = 2.1 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 -2.1 + 2x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + 2x + 2.1 + x2 = 0.0 + 2.1 Reorder the terms: -2.1 + 2.1 + 2x + x2 = 0.0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 2x + x2 = 0.0 + 2.1 2x + x2 = 0.0 + 2.1 Combine like terms: 0.0 + 2.1 = 2.1 2x + x2 = 2.1 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 = 2.1 + 1 Reorder the terms: 1 + 2x + x2 = 2.1 + 1 Combine like terms: 2.1 + 1 = 3.1 1 + 2x + x2 = 3.1 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.1 Calculate the square root of the right side: 1.760681686 Break this problem into two subproblems by setting (x + 1) equal to 1.760681686 and -1.760681686.Subproblem 1
x + 1 = 1.760681686 Simplifying x + 1 = 1.760681686 Reorder the terms: 1 + x = 1.760681686 Solving 1 + x = 1.760681686 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 = 1.760681686 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.760681686 + -1 x = 1.760681686 + -1 Combine like terms: 1.760681686 + -1 = 0.760681686 x = 0.760681686 Simplifying x = 0.760681686Subproblem 2
x + 1 = -1.760681686 Simplifying x + 1 = -1.760681686 Reorder the terms: 1 + x = -1.760681686 Solving 1 + x = -1.760681686 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 = -1.760681686 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.760681686 + -1 x = -1.760681686 + -1 Combine like terms: -1.760681686 + -1 = -2.760681686 x = -2.760681686 Simplifying x = -2.760681686Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.760681686, -2.760681686}
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