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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 = 11.583123952 X = 11.583123952 Simplifying X = 11.583123952Subproblem 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 = -21.583123952 X = -21.583123952 Simplifying X = -21.583123952Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.583123952, -21.583123952}
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