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Simplifying (x2) + -1(2x) + -50 = 249 x2 + -1(2x) + -50 = 249 Remove parenthesis around (2x) x2 + -1 * 2x + -50 = 249 Multiply -1 * 2 x2 + -2x + -50 = 249 Reorder the terms: -50 + -2x + x2 = 249 Solving -50 + -2x + x2 = 249 Solving for variable 'x'. Reorder the terms: -50 + -249 + -2x + x2 = 249 + -249 Combine like terms: -50 + -249 = -299 -299 + -2x + x2 = 249 + -249 Combine like terms: 249 + -249 = 0 -299 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '299' to each side of the equation. -299 + -2x + 299 + x2 = 0 + 299 Reorder the terms: -299 + 299 + -2x + x2 = 0 + 299 Combine like terms: -299 + 299 = 0 0 + -2x + x2 = 0 + 299 -2x + x2 = 0 + 299 Combine like terms: 0 + 299 = 299 -2x + x2 = 299 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 = 299 + 1 Reorder the terms: 1 + -2x + x2 = 299 + 1 Combine like terms: 299 + 1 = 300 1 + -2x + x2 = 300 Factor a perfect square on the left side: (x + -1)(x + -1) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + -1) equal to 17.320508076 and -17.320508076.Subproblem 1
x + -1 = 17.320508076 Simplifying x + -1 = 17.320508076 Reorder the terms: -1 + x = 17.320508076 Solving -1 + x = 17.320508076 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 = 17.320508076 + 1 Combine like terms: -1 + 1 = 0 0 + x = 17.320508076 + 1 x = 17.320508076 + 1 Combine like terms: 17.320508076 + 1 = 18.320508076 x = 18.320508076 Simplifying x = 18.320508076Subproblem 2
x + -1 = -17.320508076 Simplifying x + -1 = -17.320508076 Reorder the terms: -1 + x = -17.320508076 Solving -1 + x = -17.320508076 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 = -17.320508076 + 1 Combine like terms: -1 + 1 = 0 0 + x = -17.320508076 + 1 x = -17.320508076 + 1 Combine like terms: -17.320508076 + 1 = -16.320508076 x = -16.320508076 Simplifying x = -16.320508076Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.320508076, -16.320508076}
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