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Simplifying x2 + 10x + -2450 = 0 Reorder the terms: -2450 + 10x + x2 = 0 Solving -2450 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2450' to each side of the equation. -2450 + 10x + 2450 + x2 = 0 + 2450 Reorder the terms: -2450 + 2450 + 10x + x2 = 0 + 2450 Combine like terms: -2450 + 2450 = 0 0 + 10x + x2 = 0 + 2450 10x + x2 = 0 + 2450 Combine like terms: 0 + 2450 = 2450 10x + x2 = 2450 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 = 2450 + 25 Reorder the terms: 25 + 10x + x2 = 2450 + 25 Combine like terms: 2450 + 25 = 2475 25 + 10x + x2 = 2475 Factor a perfect square on the left side: (x + 5)(x + 5) = 2475 Calculate the square root of the right side: 49.749371855 Break this problem into two subproblems by setting (x + 5) equal to 49.749371855 and -49.749371855.Subproblem 1
x + 5 = 49.749371855 Simplifying x + 5 = 49.749371855 Reorder the terms: 5 + x = 49.749371855 Solving 5 + x = 49.749371855 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 = 49.749371855 + -5 Combine like terms: 5 + -5 = 0 0 + x = 49.749371855 + -5 x = 49.749371855 + -5 Combine like terms: 49.749371855 + -5 = 44.749371855 x = 44.749371855 Simplifying x = 44.749371855Subproblem 2
x + 5 = -49.749371855 Simplifying x + 5 = -49.749371855 Reorder the terms: 5 + x = -49.749371855 Solving 5 + x = -49.749371855 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 = -49.749371855 + -5 Combine like terms: 5 + -5 = 0 0 + x = -49.749371855 + -5 x = -49.749371855 + -5 Combine like terms: -49.749371855 + -5 = -54.749371855 x = -54.749371855 Simplifying x = -54.749371855Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.749371855, -54.749371855}
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