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Simplifying 1096.6332 = 2x2 + -1x Reorder the terms: 1096.6332 = -1x + 2x2 Solving 1096.6332 = -1x + 2x2 Solving for variable 'x'. Reorder the terms: 1096.6332 + x + -2x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 1096.6332 + x + -2x2 = 0 + 2x2 + -2x2 1096.6332 + x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1096.6332 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -548.3166 + -0.5x + x2 = 0 Move the constant term to the right: Add '548.3166' to each side of the equation. -548.3166 + -0.5x + 548.3166 + x2 = 0 + 548.3166 Reorder the terms: -548.3166 + 548.3166 + -0.5x + x2 = 0 + 548.3166 Combine like terms: -548.3166 + 548.3166 = 0.0000 0.0000 + -0.5x + x2 = 0 + 548.3166 -0.5x + x2 = 0 + 548.3166 Combine like terms: 0 + 548.3166 = 548.3166 -0.5x + x2 = 548.3166 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = 548.3166 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = 548.3166 + 0.25 Combine like terms: 548.3166 + 0.25 = 548.5666 0.25 + -0.5x + x2 = 548.5666 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 548.5666 Calculate the square root of the right side: 23.421498671 Break this problem into two subproblems by setting (x + 0.5) equal to 23.421498671 and -23.421498671.Subproblem 1
x + 0.5 = 23.421498671 Simplifying x + 0.5 = 23.421498671 Reorder the terms: 0.5 + x = 23.421498671 Solving 0.5 + x = 23.421498671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 23.421498671 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 23.421498671 + -0.5 x = 23.421498671 + -0.5 Combine like terms: 23.421498671 + -0.5 = 22.921498671 x = 22.921498671 Simplifying x = 22.921498671Subproblem 2
x + 0.5 = -23.421498671 Simplifying x + 0.5 = -23.421498671 Reorder the terms: 0.5 + x = -23.421498671 Solving 0.5 + x = -23.421498671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -23.421498671 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -23.421498671 + -0.5 x = -23.421498671 + -0.5 Combine like terms: -23.421498671 + -0.5 = -23.921498671 x = -23.921498671 Simplifying x = -23.921498671Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.921498671, -23.921498671}
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