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Simplifying x2 + -2x + -950 = 0 Reorder the terms: -950 + -2x + x2 = 0 Solving -950 + -2x + 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 + -2x + 950 + x2 = 0 + 950 Reorder the terms: -950 + 950 + -2x + x2 = 0 + 950 Combine like terms: -950 + 950 = 0 0 + -2x + x2 = 0 + 950 -2x + x2 = 0 + 950 Combine like terms: 0 + 950 = 950 -2x + x2 = 950 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 950 + 1 Reorder the terms: 1 + -2x + x2 = 950 + 1 Combine like terms: 950 + 1 = 951 1 + -2x + x2 = 951 Factor a perfect square on the left side: (x + -1)(x + -1) = 951 Calculate the square root of the right side: 30.83828789 Break this problem into two subproblems by setting (x + -1) equal to 30.83828789 and -30.83828789.Subproblem 1
x + -1 = 30.83828789 Simplifying x + -1 = 30.83828789 Reorder the terms: -1 + x = 30.83828789 Solving -1 + x = 30.83828789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 30.83828789 + 1 Combine like terms: -1 + 1 = 0 0 + x = 30.83828789 + 1 x = 30.83828789 + 1 Combine like terms: 30.83828789 + 1 = 31.83828789 x = 31.83828789 Simplifying x = 31.83828789Subproblem 2
x + -1 = -30.83828789 Simplifying x + -1 = -30.83828789 Reorder the terms: -1 + x = -30.83828789 Solving -1 + x = -30.83828789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -30.83828789 + 1 Combine like terms: -1 + 1 = 0 0 + x = -30.83828789 + 1 x = -30.83828789 + 1 Combine like terms: -30.83828789 + 1 = -29.83828789 x = -29.83828789 Simplifying x = -29.83828789Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.83828789, -29.83828789}
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