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Simplifying X * X + -102X + 504 = 0 Multiply X * X X2 + -102X + 504 = 0 Reorder the terms: 504 + -102X + X2 = 0 Solving 504 + -102X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-504' to each side of the equation. 504 + -102X + -504 + X2 = 0 + -504 Reorder the terms: 504 + -504 + -102X + X2 = 0 + -504 Combine like terms: 504 + -504 = 0 0 + -102X + X2 = 0 + -504 -102X + X2 = 0 + -504 Combine like terms: 0 + -504 = -504 -102X + X2 = -504 The X term is -102X. Take half its coefficient (-51). Square it (2601) and add it to both sides. Add '2601' to each side of the equation. -102X + 2601 + X2 = -504 + 2601 Reorder the terms: 2601 + -102X + X2 = -504 + 2601 Combine like terms: -504 + 2601 = 2097 2601 + -102X + X2 = 2097 Factor a perfect square on the left side: (X + -51)(X + -51) = 2097 Calculate the square root of the right side: 45.793012567 Break this problem into two subproblems by setting (X + -51) equal to 45.793012567 and -45.793012567.Subproblem 1
X + -51 = 45.793012567 Simplifying X + -51 = 45.793012567 Reorder the terms: -51 + X = 45.793012567 Solving -51 + X = 45.793012567 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + X = 45.793012567 + 51 Combine like terms: -51 + 51 = 0 0 + X = 45.793012567 + 51 X = 45.793012567 + 51 Combine like terms: 45.793012567 + 51 = 96.793012567 X = 96.793012567 Simplifying X = 96.793012567Subproblem 2
X + -51 = -45.793012567 Simplifying X + -51 = -45.793012567 Reorder the terms: -51 + X = -45.793012567 Solving -51 + X = -45.793012567 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + X = -45.793012567 + 51 Combine like terms: -51 + 51 = 0 0 + X = -45.793012567 + 51 X = -45.793012567 + 51 Combine like terms: -45.793012567 + 51 = 5.206987433 X = 5.206987433 Simplifying X = 5.206987433Solution
The solution to the problem is based on the solutions from the subproblems. X = {96.793012567, 5.206987433}
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