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Simplifying 1.1x2 + -3.14x + 2.24 = 0 Reorder the terms: 2.24 + -3.14x + 1.1x2 = 0 Solving 2.24 + -3.14x + 1.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.1 the coefficient of the squared term: Divide each side by '1.1'. 2.036363636 + -2.854545455x + x2 = 0 Move the constant term to the right: Add '-2.036363636' to each side of the equation. 2.036363636 + -2.854545455x + -2.036363636 + x2 = 0 + -2.036363636 Reorder the terms: 2.036363636 + -2.036363636 + -2.854545455x + x2 = 0 + -2.036363636 Combine like terms: 2.036363636 + -2.036363636 = 0.000000000 0.000000000 + -2.854545455x + x2 = 0 + -2.036363636 -2.854545455x + x2 = 0 + -2.036363636 Combine like terms: 0 + -2.036363636 = -2.036363636 -2.854545455x + x2 = -2.036363636 The x term is -2.854545455x. Take half its coefficient (-1.427272728). Square it (2.037107440) and add it to both sides. Add '2.037107440' to each side of the equation. -2.854545455x + 2.037107440 + x2 = -2.036363636 + 2.037107440 Reorder the terms: 2.037107440 + -2.854545455x + x2 = -2.036363636 + 2.037107440 Combine like terms: -2.036363636 + 2.037107440 = 0.000743804 2.037107440 + -2.854545455x + x2 = 0.000743804 Factor a perfect square on the left side: (x + -1.427272728)(x + -1.427272728) = 0.000743804 Calculate the square root of the right side: 0.02727277 Break this problem into two subproblems by setting (x + -1.427272728) equal to 0.02727277 and -0.02727277.Subproblem 1
x + -1.427272728 = 0.02727277 Simplifying x + -1.427272728 = 0.02727277 Reorder the terms: -1.427272728 + x = 0.02727277 Solving -1.427272728 + x = 0.02727277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.427272728' to each side of the equation. -1.427272728 + 1.427272728 + x = 0.02727277 + 1.427272728 Combine like terms: -1.427272728 + 1.427272728 = 0.000000000 0.000000000 + x = 0.02727277 + 1.427272728 x = 0.02727277 + 1.427272728 Combine like terms: 0.02727277 + 1.427272728 = 1.454545498 x = 1.454545498 Simplifying x = 1.454545498Subproblem 2
x + -1.427272728 = -0.02727277 Simplifying x + -1.427272728 = -0.02727277 Reorder the terms: -1.427272728 + x = -0.02727277 Solving -1.427272728 + x = -0.02727277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.427272728' to each side of the equation. -1.427272728 + 1.427272728 + x = -0.02727277 + 1.427272728 Combine like terms: -1.427272728 + 1.427272728 = 0.000000000 0.000000000 + x = -0.02727277 + 1.427272728 x = -0.02727277 + 1.427272728 Combine like terms: -0.02727277 + 1.427272728 = 1.399999958 x = 1.399999958 Simplifying x = 1.399999958Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.454545498, 1.399999958}
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