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Simplifying x2 + x + -32.7183 = 0 Reorder the terms: -32.7183 + x + x2 = 0 Solving -32.7183 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32.7183' to each side of the equation. -32.7183 + x + 32.7183 + x2 = 0 + 32.7183 Reorder the terms: -32.7183 + 32.7183 + x + x2 = 0 + 32.7183 Combine like terms: -32.7183 + 32.7183 = 0.0000 0.0000 + x + x2 = 0 + 32.7183 x + x2 = 0 + 32.7183 Combine like terms: 0 + 32.7183 = 32.7183 x + x2 = 32.7183 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. x + 0.25 + x2 = 32.7183 + 0.25 Reorder the terms: 0.25 + x + x2 = 32.7183 + 0.25 Combine like terms: 32.7183 + 0.25 = 32.9683 0.25 + x + x2 = 32.9683 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 32.9683 Calculate the square root of the right side: 5.741802853 Break this problem into two subproblems by setting (x + 0.5) equal to 5.741802853 and -5.741802853.Subproblem 1
x + 0.5 = 5.741802853 Simplifying x + 0.5 = 5.741802853 Reorder the terms: 0.5 + x = 5.741802853 Solving 0.5 + x = 5.741802853 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 = 5.741802853 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.741802853 + -0.5 x = 5.741802853 + -0.5 Combine like terms: 5.741802853 + -0.5 = 5.241802853 x = 5.241802853 Simplifying x = 5.241802853Subproblem 2
x + 0.5 = -5.741802853 Simplifying x + 0.5 = -5.741802853 Reorder the terms: 0.5 + x = -5.741802853 Solving 0.5 + x = -5.741802853 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 = -5.741802853 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.741802853 + -0.5 x = -5.741802853 + -0.5 Combine like terms: -5.741802853 + -0.5 = -6.241802853 x = -6.241802853 Simplifying x = -6.241802853Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.241802853, -6.241802853}
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