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Simplifying 4.58x2 + -10.16x + 3.91 = 0 Reorder the terms: 3.91 + -10.16x + 4.58x2 = 0 Solving 3.91 + -10.16x + 4.58x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.58 the coefficient of the squared term: Divide each side by '4.58'. 0.8537117904 + -2.218340611x + x2 = 0 Move the constant term to the right: Add '-0.8537117904' to each side of the equation. 0.8537117904 + -2.218340611x + -0.8537117904 + x2 = 0 + -0.8537117904 Reorder the terms: 0.8537117904 + -0.8537117904 + -2.218340611x + x2 = 0 + -0.8537117904 Combine like terms: 0.8537117904 + -0.8537117904 = 0.0000000000 0.0000000000 + -2.218340611x + x2 = 0 + -0.8537117904 -2.218340611x + x2 = 0 + -0.8537117904 Combine like terms: 0 + -0.8537117904 = -0.8537117904 -2.218340611x + x2 = -0.8537117904 The x term is -2.218340611x. Take half its coefficient (-1.109170306). Square it (1.230258768) and add it to both sides. Add '1.230258768' to each side of the equation. -2.218340611x + 1.230258768 + x2 = -0.8537117904 + 1.230258768 Reorder the terms: 1.230258768 + -2.218340611x + x2 = -0.8537117904 + 1.230258768 Combine like terms: -0.8537117904 + 1.230258768 = 0.3765469776 1.230258768 + -2.218340611x + x2 = 0.3765469776 Factor a perfect square on the left side: (x + -1.109170306)(x + -1.109170306) = 0.3765469776 Calculate the square root of the right side: 0.613634238 Break this problem into two subproblems by setting (x + -1.109170306) equal to 0.613634238 and -0.613634238.Subproblem 1
x + -1.109170306 = 0.613634238 Simplifying x + -1.109170306 = 0.613634238 Reorder the terms: -1.109170306 + x = 0.613634238 Solving -1.109170306 + x = 0.613634238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.109170306' to each side of the equation. -1.109170306 + 1.109170306 + x = 0.613634238 + 1.109170306 Combine like terms: -1.109170306 + 1.109170306 = 0.000000000 0.000000000 + x = 0.613634238 + 1.109170306 x = 0.613634238 + 1.109170306 Combine like terms: 0.613634238 + 1.109170306 = 1.722804544 x = 1.722804544 Simplifying x = 1.722804544Subproblem 2
x + -1.109170306 = -0.613634238 Simplifying x + -1.109170306 = -0.613634238 Reorder the terms: -1.109170306 + x = -0.613634238 Solving -1.109170306 + x = -0.613634238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.109170306' to each side of the equation. -1.109170306 + 1.109170306 + x = -0.613634238 + 1.109170306 Combine like terms: -1.109170306 + 1.109170306 = 0.000000000 0.000000000 + x = -0.613634238 + 1.109170306 x = -0.613634238 + 1.109170306 Combine like terms: -0.613634238 + 1.109170306 = 0.495536068 x = 0.495536068 Simplifying x = 0.495536068Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.722804544, 0.495536068}
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