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Simplifying x2 + -10x + -950 = 0 Reorder the terms: -950 + -10x + x2 = 0 Solving -950 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '950' to each side of the equation. -950 + -10x + 950 + x2 = 0 + 950 Reorder the terms: -950 + 950 + -10x + x2 = 0 + 950 Combine like terms: -950 + 950 = 0 0 + -10x + x2 = 0 + 950 -10x + x2 = 0 + 950 Combine like terms: 0 + 950 = 950 -10x + x2 = 950 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 = 950 + 25 Reorder the terms: 25 + -10x + x2 = 950 + 25 Combine like terms: 950 + 25 = 975 25 + -10x + x2 = 975 Factor a perfect square on the left side: (x + -5)(x + -5) = 975 Calculate the square root of the right side: 31.224989992 Break this problem into two subproblems by setting (x + -5) equal to 31.224989992 and -31.224989992.Subproblem 1
x + -5 = 31.224989992 Simplifying x + -5 = 31.224989992 Reorder the terms: -5 + x = 31.224989992 Solving -5 + x = 31.224989992 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 = 31.224989992 + 5 Combine like terms: -5 + 5 = 0 0 + x = 31.224989992 + 5 x = 31.224989992 + 5 Combine like terms: 31.224989992 + 5 = 36.224989992 x = 36.224989992 Simplifying x = 36.224989992Subproblem 2
x + -5 = -31.224989992 Simplifying x + -5 = -31.224989992 Reorder the terms: -5 + x = -31.224989992 Solving -5 + x = -31.224989992 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 = -31.224989992 + 5 Combine like terms: -5 + 5 = 0 0 + x = -31.224989992 + 5 x = -31.224989992 + 5 Combine like terms: -31.224989992 + 5 = -26.224989992 x = -26.224989992 Simplifying x = -26.224989992Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.224989992, -26.224989992}
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