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Simplifying x2 + 6x + -250 = 0 Reorder the terms: -250 + 6x + x2 = 0 Solving -250 + 6x + x2 = 0 Solving for variable 'x'. 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 = 13.093476939 x = 13.093476939 Simplifying x = 13.093476939Subproblem 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 = -19.093476939 x = -19.093476939 Simplifying x = -19.093476939Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.093476939, -19.093476939}
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