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Simplifying x2 + x + 1 = 45 Reorder the terms: 1 + x + x2 = 45 Solving 1 + x + x2 = 45 Solving for variable 'x'. Reorder the terms: 1 + -45 + x + x2 = 45 + -45 Combine like terms: 1 + -45 = -44 -44 + x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -44 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + x + x2 = 0 + 44 x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 x + x2 = 44 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 = 44 + 0.25 Reorder the terms: 0.25 + x + x2 = 44 + 0.25 Combine like terms: 44 + 0.25 = 44.25 0.25 + x + x2 = 44.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + 0.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + 0.5 = 6.652067348 Simplifying x + 0.5 = 6.652067348 Reorder the terms: 0.5 + x = 6.652067348 Solving 0.5 + x = 6.652067348 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 = 6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.652067348 + -0.5 x = 6.652067348 + -0.5 Combine like terms: 6.652067348 + -0.5 = 6.152067348 x = 6.152067348 Simplifying x = 6.152067348Subproblem 2
x + 0.5 = -6.652067348 Simplifying x + 0.5 = -6.652067348 Reorder the terms: 0.5 + x = -6.652067348 Solving 0.5 + x = -6.652067348 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 = -6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.652067348 + -0.5 x = -6.652067348 + -0.5 Combine like terms: -6.652067348 + -0.5 = -7.152067348 x = -7.152067348 Simplifying x = -7.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.152067348, -7.152067348}
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