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Simplifying x2 + -5 = 1.732050807568877x Reorder the terms: -5 + x2 = 1.732050807568877x Solving -5 + x2 = 1.732050807568877x Solving for variable 'x'. Reorder the terms: -5 + -1.732050807568877x + x2 = 1.732050807568877x + -1.732050807568877x Combine like terms: 1.732050807568877x + -1.732050807568877x = 0.000000000000000 -5 + -1.732050807568877x + x2 = 0.000000000000000 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.732050807568877x + 5 + x2 = 0.000000000000000 + 5 Reorder the terms: -5 + 5 + -1.732050807568877x + x2 = 0.000000000000000 + 5 Combine like terms: -5 + 5 = 0 0 + -1.732050807568877x + x2 = 0.000000000000000 + 5 -1.732050807568877x + x2 = 0.000000000000000 + 5 Combine like terms: 0.000000000000000 + 5 = 5 -1.732050807568877x + x2 = 5 The x term is -1.732050807568877x. Take half its coefficient (-0.8660254038). Square it (0.7500000000) and add it to both sides. Add '0.7500000000' to each side of the equation. -1.732050807568877x + 0.7500000000 + x2 = 5 + 0.7500000000 Reorder the terms: 0.7500000000 + -1.732050807568877x + x2 = 5 + 0.7500000000 Combine like terms: 5 + 0.7500000000 = 5.75 0.7500000000 + -1.732050807568877x + x2 = 5.75 Factor a perfect square on the left side: (x + -0.8660254038)(x + -0.8660254038) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + -0.8660254038) equal to 2.397915762 and -2.397915762.Subproblem 1
x + -0.8660254038 = 2.397915762 Simplifying x + -0.8660254038 = 2.397915762 Reorder the terms: -0.8660254038 + x = 2.397915762 Solving -0.8660254038 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8660254038' to each side of the equation. -0.8660254038 + 0.8660254038 + x = 2.397915762 + 0.8660254038 Combine like terms: -0.8660254038 + 0.8660254038 = 0.0000000000 0.0000000000 + x = 2.397915762 + 0.8660254038 x = 2.397915762 + 0.8660254038 Combine like terms: 2.397915762 + 0.8660254038 = 3.2639411658 x = 3.2639411658 Simplifying x = 3.2639411658Subproblem 2
x + -0.8660254038 = -2.397915762 Simplifying x + -0.8660254038 = -2.397915762 Reorder the terms: -0.8660254038 + x = -2.397915762 Solving -0.8660254038 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8660254038' to each side of the equation. -0.8660254038 + 0.8660254038 + x = -2.397915762 + 0.8660254038 Combine like terms: -0.8660254038 + 0.8660254038 = 0.0000000000 0.0000000000 + x = -2.397915762 + 0.8660254038 x = -2.397915762 + 0.8660254038 Combine like terms: -2.397915762 + 0.8660254038 = -1.5318903582 x = -1.5318903582 Simplifying x = -1.5318903582Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2639411658, -1.5318903582}
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