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Simplifying 2.0351891x2 + -2.314096938x + 0.032907838 = 0 Reorder the terms: 0.032907838 + -2.314096938x + 2.0351891x2 = 0 Solving 0.032907838 + -2.314096938x + 2.0351891x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.0351891 the coefficient of the squared term: Divide each side by '2.0351891'. 0.01616942524 + -1.137042714x + x2 = 0 Move the constant term to the right: Add '-0.01616942524' to each side of the equation. 0.01616942524 + -1.137042714x + -0.01616942524 + x2 = 0 + -0.01616942524 Reorder the terms: 0.01616942524 + -0.01616942524 + -1.137042714x + x2 = 0 + -0.01616942524 Combine like terms: 0.01616942524 + -0.01616942524 = 0.00000000000 0.00000000000 + -1.137042714x + x2 = 0 + -0.01616942524 -1.137042714x + x2 = 0 + -0.01616942524 Combine like terms: 0 + -0.01616942524 = -0.01616942524 -1.137042714x + x2 = -0.01616942524 The x term is -1.137042714x. Take half its coefficient (-0.568521357). Square it (0.3232165334) and add it to both sides. Add '0.3232165334' to each side of the equation. -1.137042714x + 0.3232165334 + x2 = -0.01616942524 + 0.3232165334 Reorder the terms: 0.3232165334 + -1.137042714x + x2 = -0.01616942524 + 0.3232165334 Combine like terms: -0.01616942524 + 0.3232165334 = 0.30704710816 0.3232165334 + -1.137042714x + x2 = 0.30704710816 Factor a perfect square on the left side: (x + -0.568521357)(x + -0.568521357) = 0.30704710816 Calculate the square root of the right side: 0.554118316 Break this problem into two subproblems by setting (x + -0.568521357) equal to 0.554118316 and -0.554118316.Subproblem 1
x + -0.568521357 = 0.554118316 Simplifying x + -0.568521357 = 0.554118316 Reorder the terms: -0.568521357 + x = 0.554118316 Solving -0.568521357 + x = 0.554118316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.568521357' to each side of the equation. -0.568521357 + 0.568521357 + x = 0.554118316 + 0.568521357 Combine like terms: -0.568521357 + 0.568521357 = 0.000000000 0.000000000 + x = 0.554118316 + 0.568521357 x = 0.554118316 + 0.568521357 Combine like terms: 0.554118316 + 0.568521357 = 1.122639673 x = 1.122639673 Simplifying x = 1.122639673Subproblem 2
x + -0.568521357 = -0.554118316 Simplifying x + -0.568521357 = -0.554118316 Reorder the terms: -0.568521357 + x = -0.554118316 Solving -0.568521357 + x = -0.554118316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.568521357' to each side of the equation. -0.568521357 + 0.568521357 + x = -0.554118316 + 0.568521357 Combine like terms: -0.568521357 + 0.568521357 = 0.000000000 0.000000000 + x = -0.554118316 + 0.568521357 x = -0.554118316 + 0.568521357 Combine like terms: -0.554118316 + 0.568521357 = 0.014403041 x = 0.014403041 Simplifying x = 0.014403041Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.122639673, 0.014403041}
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