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Simplifying x2 + 0.44x + -4.2196 = 0 Reorder the terms: -4.2196 + 0.44x + x2 = 0 Solving -4.2196 + 0.44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4.2196' to each side of the equation. -4.2196 + 0.44x + 4.2196 + x2 = 0 + 4.2196 Reorder the terms: -4.2196 + 4.2196 + 0.44x + x2 = 0 + 4.2196 Combine like terms: -4.2196 + 4.2196 = 0.0000 0.0000 + 0.44x + x2 = 0 + 4.2196 0.44x + x2 = 0 + 4.2196 Combine like terms: 0 + 4.2196 = 4.2196 0.44x + x2 = 4.2196 The x term is 0.44x. Take half its coefficient (0.22). Square it (0.0484) and add it to both sides. Add '0.0484' to each side of the equation. 0.44x + 0.0484 + x2 = 4.2196 + 0.0484 Reorder the terms: 0.0484 + 0.44x + x2 = 4.2196 + 0.0484 Combine like terms: 4.2196 + 0.0484 = 4.268 0.0484 + 0.44x + x2 = 4.268 Factor a perfect square on the left side: (x + 0.22)(x + 0.22) = 4.268 Calculate the square root of the right side: 2.065913841 Break this problem into two subproblems by setting (x + 0.22) equal to 2.065913841 and -2.065913841.Subproblem 1
x + 0.22 = 2.065913841 Simplifying x + 0.22 = 2.065913841 Reorder the terms: 0.22 + x = 2.065913841 Solving 0.22 + x = 2.065913841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.22' to each side of the equation. 0.22 + -0.22 + x = 2.065913841 + -0.22 Combine like terms: 0.22 + -0.22 = 0.00 0.00 + x = 2.065913841 + -0.22 x = 2.065913841 + -0.22 Combine like terms: 2.065913841 + -0.22 = 1.845913841 x = 1.845913841 Simplifying x = 1.845913841Subproblem 2
x + 0.22 = -2.065913841 Simplifying x + 0.22 = -2.065913841 Reorder the terms: 0.22 + x = -2.065913841 Solving 0.22 + x = -2.065913841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.22' to each side of the equation. 0.22 + -0.22 + x = -2.065913841 + -0.22 Combine like terms: 0.22 + -0.22 = 0.00 0.00 + x = -2.065913841 + -0.22 x = -2.065913841 + -0.22 Combine like terms: -2.065913841 + -0.22 = -2.285913841 x = -2.285913841 Simplifying x = -2.285913841Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.845913841, -2.285913841}
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