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Simplifying x2 + x + 1 + -15252 = 0 Reorder the terms: 1 + -15252 + x + x2 = 0 Combine like terms: 1 + -15252 = -15251 -15251 + x + x2 = 0 Solving -15251 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15251' to each side of the equation. -15251 + x + 15251 + x2 = 0 + 15251 Reorder the terms: -15251 + 15251 + x + x2 = 0 + 15251 Combine like terms: -15251 + 15251 = 0 0 + x + x2 = 0 + 15251 x + x2 = 0 + 15251 Combine like terms: 0 + 15251 = 15251 x + x2 = 15251 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 = 15251 + 0.25 Reorder the terms: 0.25 + x + x2 = 15251 + 0.25 Combine like terms: 15251 + 0.25 = 15251.25 0.25 + x + x2 = 15251.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 15251.25 Calculate the square root of the right side: 123.495951351 Break this problem into two subproblems by setting (x + 0.5) equal to 123.495951351 and -123.495951351.Subproblem 1
x + 0.5 = 123.495951351 Simplifying x + 0.5 = 123.495951351 Reorder the terms: 0.5 + x = 123.495951351 Solving 0.5 + x = 123.495951351 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 = 123.495951351 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 123.495951351 + -0.5 x = 123.495951351 + -0.5 Combine like terms: 123.495951351 + -0.5 = 122.995951351 x = 122.995951351 Simplifying x = 122.995951351Subproblem 2
x + 0.5 = -123.495951351 Simplifying x + 0.5 = -123.495951351 Reorder the terms: 0.5 + x = -123.495951351 Solving 0.5 + x = -123.495951351 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 = -123.495951351 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -123.495951351 + -0.5 x = -123.495951351 + -0.5 Combine like terms: -123.495951351 + -0.5 = -123.995951351 x = -123.995951351 Simplifying x = -123.995951351Solution
The solution to the problem is based on the solutions from the subproblems. x = {122.995951351, -123.995951351}
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