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Simplifying X2 + -1X = 29 Reorder the terms: -1X + X2 = 29 Solving -1X + X2 = 29 Solving for variable 'X'. Reorder the terms: -29 + -1X + X2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -1X + 29 + X2 = 0 + 29 Reorder the terms: -29 + 29 + -1X + X2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -1X + X2 = 0 + 29 -1X + X2 = 0 + 29 Combine like terms: 0 + 29 = 29 -1X + X2 = 29 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 = 29 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 29 + 0.25 Combine like terms: 29 + 0.25 = 29.25 0.25 + -1X + X2 = 29.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (X + -0.5) equal to 5.408326913 and -5.408326913.Subproblem 1
X + -0.5 = 5.408326913 Simplifying X + -0.5 = 5.408326913 Reorder the terms: -0.5 + X = 5.408326913 Solving -0.5 + X = 5.408326913 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 = 5.408326913 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 5.408326913 + 0.5 X = 5.408326913 + 0.5 Combine like terms: 5.408326913 + 0.5 = 5.908326913 X = 5.908326913 Simplifying X = 5.908326913Subproblem 2
X + -0.5 = -5.408326913 Simplifying X + -0.5 = -5.408326913 Reorder the terms: -0.5 + X = -5.408326913 Solving -0.5 + X = -5.408326913 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 = -5.408326913 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -5.408326913 + 0.5 X = -5.408326913 + 0.5 Combine like terms: -5.408326913 + 0.5 = -4.908326913 X = -4.908326913 Simplifying X = -4.908326913Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.908326913, -4.908326913}
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