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Simplifying 4x2 + -23x + -33 = 0 Reorder the terms: -33 + -23x + 4x2 = 0 Solving -33 + -23x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.25 + -5.75x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + -5.75x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + -5.75x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + -5.75x + x2 = 0 + 8.25 -5.75x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 -5.75x + x2 = 8.25 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 8.25 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 8.25 + 8.265625 Combine like terms: 8.25 + 8.265625 = 16.515625 8.265625 + -5.75x + x2 = 16.515625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 16.515625 Calculate the square root of the right side: 4.063942052 Break this problem into two subproblems by setting (x + -2.875) equal to 4.063942052 and -4.063942052.Subproblem 1
x + -2.875 = 4.063942052 Simplifying x + -2.875 = 4.063942052 Reorder the terms: -2.875 + x = 4.063942052 Solving -2.875 + x = 4.063942052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 4.063942052 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 4.063942052 + 2.875 x = 4.063942052 + 2.875 Combine like terms: 4.063942052 + 2.875 = 6.938942052 x = 6.938942052 Simplifying x = 6.938942052Subproblem 2
x + -2.875 = -4.063942052 Simplifying x + -2.875 = -4.063942052 Reorder the terms: -2.875 + x = -4.063942052 Solving -2.875 + x = -4.063942052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -4.063942052 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -4.063942052 + 2.875 x = -4.063942052 + 2.875 Combine like terms: -4.063942052 + 2.875 = -1.188942052 x = -1.188942052 Simplifying x = -1.188942052Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.938942052, -1.188942052}
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