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Simplifying x2 + -0.261x + -0.3689 = 0 Reorder the terms: -0.3689 + -0.261x + x2 = 0 Solving -0.3689 + -0.261x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.3689' to each side of the equation. -0.3689 + -0.261x + 0.3689 + x2 = 0 + 0.3689 Reorder the terms: -0.3689 + 0.3689 + -0.261x + x2 = 0 + 0.3689 Combine like terms: -0.3689 + 0.3689 = 0.0000 0.0000 + -0.261x + x2 = 0 + 0.3689 -0.261x + x2 = 0 + 0.3689 Combine like terms: 0 + 0.3689 = 0.3689 -0.261x + x2 = 0.3689 The x term is -0.261x. Take half its coefficient (-0.1305). Square it (0.01703025) and add it to both sides. Add '0.01703025' to each side of the equation. -0.261x + 0.01703025 + x2 = 0.3689 + 0.01703025 Reorder the terms: 0.01703025 + -0.261x + x2 = 0.3689 + 0.01703025 Combine like terms: 0.3689 + 0.01703025 = 0.38593025 0.01703025 + -0.261x + x2 = 0.38593025 Factor a perfect square on the left side: (x + -0.1305)(x + -0.1305) = 0.38593025 Calculate the square root of the right side: 0.621232847 Break this problem into two subproblems by setting (x + -0.1305) equal to 0.621232847 and -0.621232847.Subproblem 1
x + -0.1305 = 0.621232847 Simplifying x + -0.1305 = 0.621232847 Reorder the terms: -0.1305 + x = 0.621232847 Solving -0.1305 + x = 0.621232847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1305' to each side of the equation. -0.1305 + 0.1305 + x = 0.621232847 + 0.1305 Combine like terms: -0.1305 + 0.1305 = 0.0000 0.0000 + x = 0.621232847 + 0.1305 x = 0.621232847 + 0.1305 Combine like terms: 0.621232847 + 0.1305 = 0.751732847 x = 0.751732847 Simplifying x = 0.751732847Subproblem 2
x + -0.1305 = -0.621232847 Simplifying x + -0.1305 = -0.621232847 Reorder the terms: -0.1305 + x = -0.621232847 Solving -0.1305 + x = -0.621232847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1305' to each side of the equation. -0.1305 + 0.1305 + x = -0.621232847 + 0.1305 Combine like terms: -0.1305 + 0.1305 = 0.0000 0.0000 + x = -0.621232847 + 0.1305 x = -0.621232847 + 0.1305 Combine like terms: -0.621232847 + 0.1305 = -0.490732847 x = -0.490732847 Simplifying x = -0.490732847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.751732847, -0.490732847}
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