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Simplifying 2x2 + -39x + -120 = 0 Reorder the terms: -120 + -39x + 2x2 = 0 Solving -120 + -39x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60 + -19.5x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -19.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -19.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -19.5x + x2 = 0 + 60 -19.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -19.5x + x2 = 60 The x term is -19.5x. Take half its coefficient (-9.75). Square it (95.0625) and add it to both sides. Add '95.0625' to each side of the equation. -19.5x + 95.0625 + x2 = 60 + 95.0625 Reorder the terms: 95.0625 + -19.5x + x2 = 60 + 95.0625 Combine like terms: 60 + 95.0625 = 155.0625 95.0625 + -19.5x + x2 = 155.0625 Factor a perfect square on the left side: (x + -9.75)(x + -9.75) = 155.0625 Calculate the square root of the right side: 12.452409405 Break this problem into two subproblems by setting (x + -9.75) equal to 12.452409405 and -12.452409405.Subproblem 1
x + -9.75 = 12.452409405 Simplifying x + -9.75 = 12.452409405 Reorder the terms: -9.75 + x = 12.452409405 Solving -9.75 + x = 12.452409405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = 12.452409405 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = 12.452409405 + 9.75 x = 12.452409405 + 9.75 Combine like terms: 12.452409405 + 9.75 = 22.202409405 x = 22.202409405 Simplifying x = 22.202409405Subproblem 2
x + -9.75 = -12.452409405 Simplifying x + -9.75 = -12.452409405 Reorder the terms: -9.75 + x = -12.452409405 Solving -9.75 + x = -12.452409405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = -12.452409405 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = -12.452409405 + 9.75 x = -12.452409405 + 9.75 Combine like terms: -12.452409405 + 9.75 = -2.702409405 x = -2.702409405 Simplifying x = -2.702409405Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.202409405, -2.702409405}
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