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Simplifying (x + -5.732050808)(x + 2.267949192) = 0 Reorder the terms: (-5.732050808 + x)(x + 2.267949192) = 0 Reorder the terms: (-5.732050808 + x)(2.267949192 + x) = 0 Multiply (-5.732050808 + x) * (2.267949192 + x) (-5.732050808(2.267949192 + x) + x(2.267949192 + x)) = 0 ((2.267949192 * -5.732050808 + x * -5.732050808) + x(2.267949192 + x)) = 0 ((-13 + -5.732050808x) + x(2.267949192 + x)) = 0 (-13 + -5.732050808x + (2.267949192 * x + x * x)) = 0 (-13 + -5.732050808x + (2.267949192x + x2)) = 0 Combine like terms: -5.732050808x + 2.267949192x = -3.464101616x (-13 + -3.464101616x + x2) = 0 Solving -13 + -3.464101616x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -3.464101616x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -3.464101616x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3.464101616x + x2 = 0 + 13 -3.464101616x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -3.464101616x + x2 = 13 The x term is -3.464101616x. Take half its coefficient (-1.732050808). Square it (3.000000001) and add it to both sides. Add '3.000000001' to each side of the equation. -3.464101616x + 3.000000001 + x2 = 13 + 3.000000001 Reorder the terms: 3.000000001 + -3.464101616x + x2 = 13 + 3.000000001 Combine like terms: 13 + 3.000000001 = 16.000000001 3.000000001 + -3.464101616x + x2 = 16.000000001 Factor a perfect square on the left side: (x + -1.732050808)(x + -1.732050808) = 16.000000001 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -1.732050808) equal to 4 and -4.Subproblem 1
x + -1.732050808 = 4 Simplifying x + -1.732050808 = 4 Reorder the terms: -1.732050808 + x = 4 Solving -1.732050808 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.732050808' to each side of the equation. -1.732050808 + 1.732050808 + x = 4 + 1.732050808 Combine like terms: -1.732050808 + 1.732050808 = 0.000000000 0.000000000 + x = 4 + 1.732050808 x = 4 + 1.732050808 Combine like terms: 4 + 1.732050808 = 5.732050808 x = 5.732050808 Simplifying x = 5.732050808Subproblem 2
x + -1.732050808 = -4 Simplifying x + -1.732050808 = -4 Reorder the terms: -1.732050808 + x = -4 Solving -1.732050808 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.732050808' to each side of the equation. -1.732050808 + 1.732050808 + x = -4 + 1.732050808 Combine like terms: -1.732050808 + 1.732050808 = 0.000000000 0.000000000 + x = -4 + 1.732050808 x = -4 + 1.732050808 Combine like terms: -4 + 1.732050808 = -2.267949192 x = -2.267949192 Simplifying x = -2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.732050808, -2.267949192}
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