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Simplifying X2 + X + 1 = 36 Reorder the terms: 1 + X + X2 = 36 Solving 1 + X + X2 = 36 Solving for variable 'X'. Reorder the terms: 1 + -36 + X + X2 = 36 + -36 Combine like terms: 1 + -36 = -35 -35 + X + X2 = 36 + -36 Combine like terms: 36 + -36 = 0 -35 + X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + X + 35 + X2 = 0 + 35 Reorder the terms: -35 + 35 + X + X2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + X + X2 = 0 + 35 X + X2 = 0 + 35 Combine like terms: 0 + 35 = 35 X + X2 = 35 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 = 35 + 0.25 Reorder the terms: 0.25 + X + X2 = 35 + 0.25 Combine like terms: 35 + 0.25 = 35.25 0.25 + X + X2 = 35.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (X + 0.5) equal to 5.937171044 and -5.937171044.Subproblem 1
X + 0.5 = 5.937171044 Simplifying X + 0.5 = 5.937171044 Reorder the terms: 0.5 + X = 5.937171044 Solving 0.5 + X = 5.937171044 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 = 5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 5.937171044 + -0.5 X = 5.937171044 + -0.5 Combine like terms: 5.937171044 + -0.5 = 5.437171044 X = 5.437171044 Simplifying X = 5.437171044Subproblem 2
X + 0.5 = -5.937171044 Simplifying X + 0.5 = -5.937171044 Reorder the terms: 0.5 + X = -5.937171044 Solving 0.5 + X = -5.937171044 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 = -5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -5.937171044 + -0.5 X = -5.937171044 + -0.5 Combine like terms: -5.937171044 + -0.5 = -6.437171044 X = -6.437171044 Simplifying X = -6.437171044Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.437171044, -6.437171044}
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