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Simplifying x2 + 1 = 42 + -1x Reorder the terms: 1 + x2 = 42 + -1x Solving 1 + x2 = 42 + -1x Solving for variable 'x'. Reorder the terms: 1 + -42 + x + x2 = 42 + -1x + -42 + x Combine like terms: 1 + -42 = -41 -41 + x + x2 = 42 + -1x + -42 + x Reorder the terms: -41 + x + x2 = 42 + -42 + -1x + x Combine like terms: 42 + -42 = 0 -41 + x + x2 = 0 + -1x + x -41 + x + x2 = -1x + x Combine like terms: -1x + x = 0 -41 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + x + x2 = 0 + 41 x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 x + x2 = 41 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 = 41 + 0.25 Reorder the terms: 0.25 + x + x2 = 41 + 0.25 Combine like terms: 41 + 0.25 = 41.25 0.25 + x + x2 = 41.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + 0.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + 0.5 = 6.422616289 Simplifying x + 0.5 = 6.422616289 Reorder the terms: 0.5 + x = 6.422616289 Solving 0.5 + x = 6.422616289 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 = 6.422616289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.422616289 + -0.5 x = 6.422616289 + -0.5 Combine like terms: 6.422616289 + -0.5 = 5.922616289 x = 5.922616289 Simplifying x = 5.922616289Subproblem 2
x + 0.5 = -6.422616289 Simplifying x + 0.5 = -6.422616289 Reorder the terms: 0.5 + x = -6.422616289 Solving 0.5 + x = -6.422616289 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 = -6.422616289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.422616289 + -0.5 x = -6.422616289 + -0.5 Combine like terms: -6.422616289 + -0.5 = -6.922616289 x = -6.922616289 Simplifying x = -6.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.922616289, -6.922616289}
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