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Simplifying x2 = x + 38 Reorder the terms: x2 = 38 + x Solving x2 = 38 + x Solving for variable 'x'. Reorder the terms: -38 + -1x + x2 = 38 + x + -38 + -1x Reorder the terms: -38 + -1x + x2 = 38 + -38 + x + -1x Combine like terms: 38 + -38 = 0 -38 + -1x + x2 = 0 + x + -1x -38 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -38 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -1x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -1x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -1x + x2 = 0 + 38 -1x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -1x + x2 = 38 The x term is -1x. 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. -1x + 0.25 + x2 = 38 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 38 + 0.25 Combine like terms: 38 + 0.25 = 38.25 0.25 + -1x + 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 = 6.684658438 x = 6.684658438 Simplifying x = 6.684658438Subproblem 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 = -5.684658438 x = -5.684658438 Simplifying x = -5.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.684658438, -5.684658438}
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