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Simplifying x2 + -10x + -250 = 0 Reorder the terms: -250 + -10x + x2 = 0 Solving -250 + -10x + 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 + -10x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -10x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -10x + x2 = 0 + 250 -10x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -10x + x2 = 250 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 250 + 25 Reorder the terms: 25 + -10x + x2 = 250 + 25 Combine like terms: 250 + 25 = 275 25 + -10x + x2 = 275 Factor a perfect square on the left side: (x + -5)(x + -5) = 275 Calculate the square root of the right side: 16.583123952 Break this problem into two subproblems by setting (x + -5) equal to 16.583123952 and -16.583123952.Subproblem 1
x + -5 = 16.583123952 Simplifying x + -5 = 16.583123952 Reorder the terms: -5 + x = 16.583123952 Solving -5 + x = 16.583123952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 16.583123952 + 5 Combine like terms: -5 + 5 = 0 0 + x = 16.583123952 + 5 x = 16.583123952 + 5 Combine like terms: 16.583123952 + 5 = 21.583123952 x = 21.583123952 Simplifying x = 21.583123952Subproblem 2
x + -5 = -16.583123952 Simplifying x + -5 = -16.583123952 Reorder the terms: -5 + x = -16.583123952 Solving -5 + x = -16.583123952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -16.583123952 + 5 Combine like terms: -5 + 5 = 0 0 + x = -16.583123952 + 5 x = -16.583123952 + 5 Combine like terms: -16.583123952 + 5 = -11.583123952 x = -11.583123952 Simplifying x = -11.583123952Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.583123952, -11.583123952}
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