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Simplifying x2 + x + -4 = -2.561552813 Reorder the terms: -4 + x + x2 = -2.561552813 Solving -4 + x + x2 = -2.561552813 Solving for variable 'x'. Reorder the terms: -4 + 2.561552813 + x + x2 = -2.561552813 + 2.561552813 Combine like terms: -4 + 2.561552813 = -1.438447187 -1.438447187 + x + x2 = -2.561552813 + 2.561552813 Combine like terms: -2.561552813 + 2.561552813 = 0.000000000 -1.438447187 + x + x2 = 0.000000000 Begin completing the square. Move the constant term to the right: Add '1.438447187' to each side of the equation. -1.438447187 + x + 1.438447187 + x2 = 0.000000000 + 1.438447187 Reorder the terms: -1.438447187 + 1.438447187 + x + x2 = 0.000000000 + 1.438447187 Combine like terms: -1.438447187 + 1.438447187 = 0.000000000 0.000000000 + x + x2 = 0.000000000 + 1.438447187 x + x2 = 0.000000000 + 1.438447187 Combine like terms: 0.000000000 + 1.438447187 = 1.438447187 x + x2 = 1.438447187 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 = 1.438447187 + 0.25 Reorder the terms: 0.25 + x + x2 = 1.438447187 + 0.25 Combine like terms: 1.438447187 + 0.25 = 1.688447187 0.25 + x + x2 = 1.688447187 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.688447187 Calculate the square root of the right side: 1.299402627 Break this problem into two subproblems by setting (x + 0.5) equal to 1.299402627 and -1.299402627.Subproblem 1
x + 0.5 = 1.299402627 Simplifying x + 0.5 = 1.299402627 Reorder the terms: 0.5 + x = 1.299402627 Solving 0.5 + x = 1.299402627 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 = 1.299402627 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.299402627 + -0.5 x = 1.299402627 + -0.5 Combine like terms: 1.299402627 + -0.5 = 0.799402627 x = 0.799402627 Simplifying x = 0.799402627Subproblem 2
x + 0.5 = -1.299402627 Simplifying x + 0.5 = -1.299402627 Reorder the terms: 0.5 + x = -1.299402627 Solving 0.5 + x = -1.299402627 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 = -1.299402627 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.299402627 + -0.5 x = -1.299402627 + -0.5 Combine like terms: -1.299402627 + -0.5 = -1.799402627 x = -1.799402627 Simplifying x = -1.799402627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.799402627, -1.799402627}
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