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Simplifying x2 + -2x = 9504 Reorder the terms: -2x + x2 = 9504 Solving -2x + x2 = 9504 Solving for variable 'x'. Reorder the terms: -9504 + -2x + x2 = 9504 + -9504 Combine like terms: 9504 + -9504 = 0 -9504 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9504' to each side of the equation. -9504 + -2x + 9504 + x2 = 0 + 9504 Reorder the terms: -9504 + 9504 + -2x + x2 = 0 + 9504 Combine like terms: -9504 + 9504 = 0 0 + -2x + x2 = 0 + 9504 -2x + x2 = 0 + 9504 Combine like terms: 0 + 9504 = 9504 -2x + x2 = 9504 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 9504 + 1 Reorder the terms: 1 + -2x + x2 = 9504 + 1 Combine like terms: 9504 + 1 = 9505 1 + -2x + x2 = 9505 Factor a perfect square on the left side: (x + -1)(x + -1) = 9505 Calculate the square root of the right side: 97.493589533 Break this problem into two subproblems by setting (x + -1) equal to 97.493589533 and -97.493589533.Subproblem 1
x + -1 = 97.493589533 Simplifying x + -1 = 97.493589533 Reorder the terms: -1 + x = 97.493589533 Solving -1 + x = 97.493589533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 97.493589533 + 1 Combine like terms: -1 + 1 = 0 0 + x = 97.493589533 + 1 x = 97.493589533 + 1 Combine like terms: 97.493589533 + 1 = 98.493589533 x = 98.493589533 Simplifying x = 98.493589533Subproblem 2
x + -1 = -97.493589533 Simplifying x + -1 = -97.493589533 Reorder the terms: -1 + x = -97.493589533 Solving -1 + x = -97.493589533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -97.493589533 + 1 Combine like terms: -1 + 1 = 0 0 + x = -97.493589533 + 1 x = -97.493589533 + 1 Combine like terms: -97.493589533 + 1 = -96.493589533 x = -96.493589533 Simplifying x = -96.493589533Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.493589533, -96.493589533}
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