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Simplifying x2 + -3x + -232 = 0 Reorder the terms: -232 + -3x + x2 = 0 Solving -232 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '232' to each side of the equation. -232 + -3x + 232 + x2 = 0 + 232 Reorder the terms: -232 + 232 + -3x + x2 = 0 + 232 Combine like terms: -232 + 232 = 0 0 + -3x + x2 = 0 + 232 -3x + x2 = 0 + 232 Combine like terms: 0 + 232 = 232 -3x + x2 = 232 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 = 232 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 232 + 2.25 Combine like terms: 232 + 2.25 = 234.25 2.25 + -3x + x2 = 234.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 234.25 Calculate the square root of the right side: 15.305227865 Break this problem into two subproblems by setting (x + -1.5) equal to 15.305227865 and -15.305227865.Subproblem 1
x + -1.5 = 15.305227865 Simplifying x + -1.5 = 15.305227865 Reorder the terms: -1.5 + x = 15.305227865 Solving -1.5 + x = 15.305227865 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 = 15.305227865 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 15.305227865 + 1.5 x = 15.305227865 + 1.5 Combine like terms: 15.305227865 + 1.5 = 16.805227865 x = 16.805227865 Simplifying x = 16.805227865Subproblem 2
x + -1.5 = -15.305227865 Simplifying x + -1.5 = -15.305227865 Reorder the terms: -1.5 + x = -15.305227865 Solving -1.5 + x = -15.305227865 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 = -15.305227865 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -15.305227865 + 1.5 x = -15.305227865 + 1.5 Combine like terms: -15.305227865 + 1.5 = -13.805227865 x = -13.805227865 Simplifying x = -13.805227865Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.805227865, -13.805227865}
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