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Simplifying x2 + -4.45x + 2 = 0 Reorder the terms: 2 + -4.45x + x2 = 0 Solving 2 + -4.45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4.45x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4.45x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4.45x + x2 = 0 + -2 -4.45x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4.45x + x2 = -2 The x term is -4.45x. Take half its coefficient (-2.225). Square it (4.950625) and add it to both sides. Add '4.950625' to each side of the equation. -4.45x + 4.950625 + x2 = -2 + 4.950625 Reorder the terms: 4.950625 + -4.45x + x2 = -2 + 4.950625 Combine like terms: -2 + 4.950625 = 2.950625 4.950625 + -4.45x + x2 = 2.950625 Factor a perfect square on the left side: (x + -2.225)(x + -2.225) = 2.950625 Calculate the square root of the right side: 1.717738339 Break this problem into two subproblems by setting (x + -2.225) equal to 1.717738339 and -1.717738339.Subproblem 1
x + -2.225 = 1.717738339 Simplifying x + -2.225 = 1.717738339 Reorder the terms: -2.225 + x = 1.717738339 Solving -2.225 + x = 1.717738339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.225' to each side of the equation. -2.225 + 2.225 + x = 1.717738339 + 2.225 Combine like terms: -2.225 + 2.225 = 0.000 0.000 + x = 1.717738339 + 2.225 x = 1.717738339 + 2.225 Combine like terms: 1.717738339 + 2.225 = 3.942738339 x = 3.942738339 Simplifying x = 3.942738339Subproblem 2
x + -2.225 = -1.717738339 Simplifying x + -2.225 = -1.717738339 Reorder the terms: -2.225 + x = -1.717738339 Solving -2.225 + x = -1.717738339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.225' to each side of the equation. -2.225 + 2.225 + x = -1.717738339 + 2.225 Combine like terms: -2.225 + 2.225 = 0.000 0.000 + x = -1.717738339 + 2.225 x = -1.717738339 + 2.225 Combine like terms: -1.717738339 + 2.225 = 0.507261661 x = 0.507261661 Simplifying x = 0.507261661Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.942738339, 0.507261661}
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