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Simplifying 3.454x2 + -4.038x + 0.36 = 0 Reorder the terms: 0.36 + -4.038x + 3.454x2 = 0 Solving 0.36 + -4.038x + 3.454x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.454 the coefficient of the squared term: Divide each side by '3.454'. 0.1042269832 + -1.169079328x + x2 = 0 Move the constant term to the right: Add '-0.1042269832' to each side of the equation. 0.1042269832 + -1.169079328x + -0.1042269832 + x2 = 0 + -0.1042269832 Reorder the terms: 0.1042269832 + -0.1042269832 + -1.169079328x + x2 = 0 + -0.1042269832 Combine like terms: 0.1042269832 + -0.1042269832 = 0.0000000000 0.0000000000 + -1.169079328x + x2 = 0 + -0.1042269832 -1.169079328x + x2 = 0 + -0.1042269832 Combine like terms: 0 + -0.1042269832 = -0.1042269832 -1.169079328x + x2 = -0.1042269832 The x term is -1.169079328x. Take half its coefficient (-0.584539664). Square it (0.3416866188) and add it to both sides. Add '0.3416866188' to each side of the equation. -1.169079328x + 0.3416866188 + x2 = -0.1042269832 + 0.3416866188 Reorder the terms: 0.3416866188 + -1.169079328x + x2 = -0.1042269832 + 0.3416866188 Combine like terms: -0.1042269832 + 0.3416866188 = 0.2374596356 0.3416866188 + -1.169079328x + x2 = 0.2374596356 Factor a perfect square on the left side: (x + -0.584539664)(x + -0.584539664) = 0.2374596356 Calculate the square root of the right side: 0.487298302 Break this problem into two subproblems by setting (x + -0.584539664) equal to 0.487298302 and -0.487298302.Subproblem 1
x + -0.584539664 = 0.487298302 Simplifying x + -0.584539664 = 0.487298302 Reorder the terms: -0.584539664 + x = 0.487298302 Solving -0.584539664 + x = 0.487298302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.584539664' to each side of the equation. -0.584539664 + 0.584539664 + x = 0.487298302 + 0.584539664 Combine like terms: -0.584539664 + 0.584539664 = 0.000000000 0.000000000 + x = 0.487298302 + 0.584539664 x = 0.487298302 + 0.584539664 Combine like terms: 0.487298302 + 0.584539664 = 1.071837966 x = 1.071837966 Simplifying x = 1.071837966Subproblem 2
x + -0.584539664 = -0.487298302 Simplifying x + -0.584539664 = -0.487298302 Reorder the terms: -0.584539664 + x = -0.487298302 Solving -0.584539664 + x = -0.487298302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.584539664' to each side of the equation. -0.584539664 + 0.584539664 + x = -0.487298302 + 0.584539664 Combine like terms: -0.584539664 + 0.584539664 = 0.000000000 0.000000000 + x = -0.487298302 + 0.584539664 x = -0.487298302 + 0.584539664 Combine like terms: -0.487298302 + 0.584539664 = 0.097241362 x = 0.097241362 Simplifying x = 0.097241362Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.071837966, 0.097241362}
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