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Simplifying x2 + -5x + -250 = x Reorder the terms: -250 + -5x + x2 = x Solving -250 + -5x + x2 = x Solving for variable 'x'. Reorder the terms: -250 + -5x + -1x + x2 = x + -1x Combine like terms: -5x + -1x = -6x -250 + -6x + x2 = x + -1x Combine like terms: x + -1x = 0 -250 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + -6x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -6x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -6x + x2 = 0 + 250 -6x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -6x + x2 = 250 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 250 + 9 Reorder the terms: 9 + -6x + x2 = 250 + 9 Combine like terms: 250 + 9 = 259 9 + -6x + x2 = 259 Factor a perfect square on the left side: (x + -3)(x + -3) = 259 Calculate the square root of the right side: 16.093476939 Break this problem into two subproblems by setting (x + -3) equal to 16.093476939 and -16.093476939.Subproblem 1
x + -3 = 16.093476939 Simplifying x + -3 = 16.093476939 Reorder the terms: -3 + x = 16.093476939 Solving -3 + x = 16.093476939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 16.093476939 + 3 Combine like terms: -3 + 3 = 0 0 + x = 16.093476939 + 3 x = 16.093476939 + 3 Combine like terms: 16.093476939 + 3 = 19.093476939 x = 19.093476939 Simplifying x = 19.093476939Subproblem 2
x + -3 = -16.093476939 Simplifying x + -3 = -16.093476939 Reorder the terms: -3 + x = -16.093476939 Solving -3 + x = -16.093476939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -16.093476939 + 3 Combine like terms: -3 + 3 = 0 0 + x = -16.093476939 + 3 x = -16.093476939 + 3 Combine like terms: -16.093476939 + 3 = -13.093476939 x = -13.093476939 Simplifying x = -13.093476939Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.093476939, -13.093476939}
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