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Simplifying x2 + -3x + -175 = 0 Reorder the terms: -175 + -3x + x2 = 0 Solving -175 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + -3x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + -3x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + -3x + x2 = 0 + 175 -3x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 -3x + x2 = 175 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 175 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 175 + 2.25 Combine like terms: 175 + 2.25 = 177.25 2.25 + -3x + x2 = 177.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 177.25 Calculate the square root of the right side: 13.313526956 Break this problem into two subproblems by setting (x + -1.5) equal to 13.313526956 and -13.313526956.Subproblem 1
x + -1.5 = 13.313526956 Simplifying x + -1.5 = 13.313526956 Reorder the terms: -1.5 + x = 13.313526956 Solving -1.5 + x = 13.313526956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 13.313526956 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 13.313526956 + 1.5 x = 13.313526956 + 1.5 Combine like terms: 13.313526956 + 1.5 = 14.813526956 x = 14.813526956 Simplifying x = 14.813526956Subproblem 2
x + -1.5 = -13.313526956 Simplifying x + -1.5 = -13.313526956 Reorder the terms: -1.5 + x = -13.313526956 Solving -1.5 + x = -13.313526956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -13.313526956 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -13.313526956 + 1.5 x = -13.313526956 + 1.5 Combine like terms: -13.313526956 + 1.5 = -11.813526956 x = -11.813526956 Simplifying x = -11.813526956Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.813526956, -11.813526956}
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