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Simplifying x2 + -35x + -250 = 0 Reorder the terms: -250 + -35x + x2 = 0 Solving -250 + -35x + 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 + -35x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -35x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -35x + x2 = 0 + 250 -35x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -35x + x2 = 250 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = 250 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 250 + 306.25 Combine like terms: 250 + 306.25 = 556.25 306.25 + -35x + x2 = 556.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 556.25 Calculate the square root of the right side: 23.58495283 Break this problem into two subproblems by setting (x + -17.5) equal to 23.58495283 and -23.58495283.Subproblem 1
x + -17.5 = 23.58495283 Simplifying x + -17.5 = 23.58495283 Reorder the terms: -17.5 + x = 23.58495283 Solving -17.5 + x = 23.58495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 23.58495283 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 23.58495283 + 17.5 x = 23.58495283 + 17.5 Combine like terms: 23.58495283 + 17.5 = 41.08495283 x = 41.08495283 Simplifying x = 41.08495283Subproblem 2
x + -17.5 = -23.58495283 Simplifying x + -17.5 = -23.58495283 Reorder the terms: -17.5 + x = -23.58495283 Solving -17.5 + x = -23.58495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -23.58495283 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -23.58495283 + 17.5 x = -23.58495283 + 17.5 Combine like terms: -23.58495283 + 17.5 = -6.08495283 x = -6.08495283 Simplifying x = -6.08495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.08495283, -6.08495283}
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