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Simplifying x2 + 4.05x + -0.8019 = 0 Reorder the terms: -0.8019 + 4.05x + x2 = 0 Solving -0.8019 + 4.05x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.8019' to each side of the equation. -0.8019 + 4.05x + 0.8019 + x2 = 0 + 0.8019 Reorder the terms: -0.8019 + 0.8019 + 4.05x + x2 = 0 + 0.8019 Combine like terms: -0.8019 + 0.8019 = 0.0000 0.0000 + 4.05x + x2 = 0 + 0.8019 4.05x + x2 = 0 + 0.8019 Combine like terms: 0 + 0.8019 = 0.8019 4.05x + x2 = 0.8019 The x term is 4.05x. Take half its coefficient (2.025). Square it (4.100625) and add it to both sides. Add '4.100625' to each side of the equation. 4.05x + 4.100625 + x2 = 0.8019 + 4.100625 Reorder the terms: 4.100625 + 4.05x + x2 = 0.8019 + 4.100625 Combine like terms: 0.8019 + 4.100625 = 4.902525 4.100625 + 4.05x + x2 = 4.902525 Factor a perfect square on the left side: (x + 2.025)(x + 2.025) = 4.902525 Calculate the square root of the right side: 2.214164628 Break this problem into two subproblems by setting (x + 2.025) equal to 2.214164628 and -2.214164628.Subproblem 1
x + 2.025 = 2.214164628 Simplifying x + 2.025 = 2.214164628 Reorder the terms: 2.025 + x = 2.214164628 Solving 2.025 + x = 2.214164628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.025' to each side of the equation. 2.025 + -2.025 + x = 2.214164628 + -2.025 Combine like terms: 2.025 + -2.025 = 0.000 0.000 + x = 2.214164628 + -2.025 x = 2.214164628 + -2.025 Combine like terms: 2.214164628 + -2.025 = 0.189164628 x = 0.189164628 Simplifying x = 0.189164628Subproblem 2
x + 2.025 = -2.214164628 Simplifying x + 2.025 = -2.214164628 Reorder the terms: 2.025 + x = -2.214164628 Solving 2.025 + x = -2.214164628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.025' to each side of the equation. 2.025 + -2.025 + x = -2.214164628 + -2.025 Combine like terms: 2.025 + -2.025 = 0.000 0.000 + x = -2.214164628 + -2.025 x = -2.214164628 + -2.025 Combine like terms: -2.214164628 + -2.025 = -4.239164628 x = -4.239164628 Simplifying x = -4.239164628Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.189164628, -4.239164628}
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