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Simplifying X2 + X = 38 Reorder the terms: X + X2 = 38 Solving X + X2 = 38 Solving for variable 'X'. Reorder the terms: -38 + X + X2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + X + 38 + X2 = 0 + 38 Reorder the terms: -38 + 38 + X + X2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + X + X2 = 0 + 38 X + X2 = 0 + 38 Combine like terms: 0 + 38 = 38 X + X2 = 38 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 = 38 + 0.25 Reorder the terms: 0.25 + X + X2 = 38 + 0.25 Combine like terms: 38 + 0.25 = 38.25 0.25 + X + X2 = 38.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (X + 0.5) equal to 6.184658438 and -6.184658438.Subproblem 1
X + 0.5 = 6.184658438 Simplifying X + 0.5 = 6.184658438 Reorder the terms: 0.5 + X = 6.184658438 Solving 0.5 + X = 6.184658438 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 = 6.184658438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 6.184658438 + -0.5 X = 6.184658438 + -0.5 Combine like terms: 6.184658438 + -0.5 = 5.684658438 X = 5.684658438 Simplifying X = 5.684658438Subproblem 2
X + 0.5 = -6.184658438 Simplifying X + 0.5 = -6.184658438 Reorder the terms: 0.5 + X = -6.184658438 Solving 0.5 + X = -6.184658438 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 = -6.184658438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -6.184658438 + -0.5 X = -6.184658438 + -0.5 Combine like terms: -6.184658438 + -0.5 = -6.684658438 X = -6.684658438 Simplifying X = -6.684658438Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.684658438, -6.684658438}
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