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Simplifying 3.85x2 + 1.4x + -0.6 = 0 Reorder the terms: -0.6 + 1.4x + 3.85x2 = 0 Solving -0.6 + 1.4x + 3.85x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.85 the coefficient of the squared term: Divide each side by '3.85'. -0.1558441558 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.1558441558' to each side of the equation. -0.1558441558 + 0.3636363636x + 0.1558441558 + x2 = 0 + 0.1558441558 Reorder the terms: -0.1558441558 + 0.1558441558 + 0.3636363636x + x2 = 0 + 0.1558441558 Combine like terms: -0.1558441558 + 0.1558441558 = 0.0000000000 0.0000000000 + 0.3636363636x + x2 = 0 + 0.1558441558 0.3636363636x + x2 = 0 + 0.1558441558 Combine like terms: 0 + 0.1558441558 = 0.1558441558 0.3636363636x + x2 = 0.1558441558 The x term is 0.3636363636x. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636x + 0.03305785123 + x2 = 0.1558441558 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 0.1558441558 + 0.03305785123 Combine like terms: 0.1558441558 + 0.03305785123 = 0.18890200703 0.03305785123 + 0.3636363636x + x2 = 0.18890200703 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 0.18890200703 Calculate the square root of the right side: 0.434628585 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 0.434628585 and -0.434628585.Subproblem 1
x + 0.1818181818 = 0.434628585 Simplifying x + 0.1818181818 = 0.434628585 Reorder the terms: 0.1818181818 + x = 0.434628585 Solving 0.1818181818 + x = 0.434628585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 0.434628585 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 0.434628585 + -0.1818181818 x = 0.434628585 + -0.1818181818 Combine like terms: 0.434628585 + -0.1818181818 = 0.2528104032 x = 0.2528104032 Simplifying x = 0.2528104032Subproblem 2
x + 0.1818181818 = -0.434628585 Simplifying x + 0.1818181818 = -0.434628585 Reorder the terms: 0.1818181818 + x = -0.434628585 Solving 0.1818181818 + x = -0.434628585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -0.434628585 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -0.434628585 + -0.1818181818 x = -0.434628585 + -0.1818181818 Combine like terms: -0.434628585 + -0.1818181818 = -0.6164467668 x = -0.6164467668 Simplifying x = -0.6164467668Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2528104032, -0.6164467668}
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