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Simplifying x2 + -4.4x + 2.3 = 0 Reorder the terms: 2.3 + -4.4x + x2 = 0 Solving 2.3 + -4.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.3' to each side of the equation. 2.3 + -4.4x + -2.3 + x2 = 0 + -2.3 Reorder the terms: 2.3 + -2.3 + -4.4x + x2 = 0 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + -4.4x + x2 = 0 + -2.3 -4.4x + x2 = 0 + -2.3 Combine like terms: 0 + -2.3 = -2.3 -4.4x + x2 = -2.3 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = -2.3 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -2.3 + 4.84 Combine like terms: -2.3 + 4.84 = 2.54 4.84 + -4.4x + x2 = 2.54 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 2.54 Calculate the square root of the right side: 1.593737745 Break this problem into two subproblems by setting (x + -2.2) equal to 1.593737745 and -1.593737745.Subproblem 1
x + -2.2 = 1.593737745 Simplifying x + -2.2 = 1.593737745 Reorder the terms: -2.2 + x = 1.593737745 Solving -2.2 + x = 1.593737745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 1.593737745 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 1.593737745 + 2.2 x = 1.593737745 + 2.2 Combine like terms: 1.593737745 + 2.2 = 3.793737745 x = 3.793737745 Simplifying x = 3.793737745Subproblem 2
x + -2.2 = -1.593737745 Simplifying x + -2.2 = -1.593737745 Reorder the terms: -2.2 + x = -1.593737745 Solving -2.2 + x = -1.593737745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -1.593737745 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -1.593737745 + 2.2 x = -1.593737745 + 2.2 Combine like terms: -1.593737745 + 2.2 = 0.606262255 x = 0.606262255 Simplifying x = 0.606262255Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.793737745, 0.606262255}
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