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Simplifying x2 + x + -3661 = 0 Reorder the terms: -3661 + x + x2 = 0 Solving -3661 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3661' to each side of the equation. -3661 + x + 3661 + x2 = 0 + 3661 Reorder the terms: -3661 + 3661 + x + x2 = 0 + 3661 Combine like terms: -3661 + 3661 = 0 0 + x + x2 = 0 + 3661 x + x2 = 0 + 3661 Combine like terms: 0 + 3661 = 3661 x + x2 = 3661 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 = 3661 + 0.25 Reorder the terms: 0.25 + x + x2 = 3661 + 0.25 Combine like terms: 3661 + 0.25 = 3661.25 0.25 + x + x2 = 3661.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3661.25 Calculate the square root of the right side: 60.508263898 Break this problem into two subproblems by setting (x + 0.5) equal to 60.508263898 and -60.508263898.Subproblem 1
x + 0.5 = 60.508263898 Simplifying x + 0.5 = 60.508263898 Reorder the terms: 0.5 + x = 60.508263898 Solving 0.5 + x = 60.508263898 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 = 60.508263898 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 60.508263898 + -0.5 x = 60.508263898 + -0.5 Combine like terms: 60.508263898 + -0.5 = 60.008263898 x = 60.008263898 Simplifying x = 60.008263898Subproblem 2
x + 0.5 = -60.508263898 Simplifying x + 0.5 = -60.508263898 Reorder the terms: 0.5 + x = -60.508263898 Solving 0.5 + x = -60.508263898 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 = -60.508263898 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -60.508263898 + -0.5 x = -60.508263898 + -0.5 Combine like terms: -60.508263898 + -0.5 = -61.008263898 x = -61.008263898 Simplifying x = -61.008263898Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.008263898, -61.008263898}
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