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Simplifying 3x2 + -68x + -192 = 0 Reorder the terms: -192 + -68x + 3x2 = 0 Solving -192 + -68x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -64 + -22.66666667x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + -22.66666667x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -22.66666667x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -22.66666667x + x2 = 0 + 64 -22.66666667x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -22.66666667x + x2 = 64 The x term is -22.66666667x. Take half its coefficient (-11.33333334). Square it (128.4444446) and add it to both sides. Add '128.4444446' to each side of the equation. -22.66666667x + 128.4444446 + x2 = 64 + 128.4444446 Reorder the terms: 128.4444446 + -22.66666667x + x2 = 64 + 128.4444446 Combine like terms: 64 + 128.4444446 = 192.4444446 128.4444446 + -22.66666667x + x2 = 192.4444446 Factor a perfect square on the left side: (x + -11.33333334)(x + -11.33333334) = 192.4444446 Calculate the square root of the right side: 13.872434703 Break this problem into two subproblems by setting (x + -11.33333334) equal to 13.872434703 and -13.872434703.Subproblem 1
x + -11.33333334 = 13.872434703 Simplifying x + -11.33333334 = 13.872434703 Reorder the terms: -11.33333334 + x = 13.872434703 Solving -11.33333334 + x = 13.872434703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = 13.872434703 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = 13.872434703 + 11.33333334 x = 13.872434703 + 11.33333334 Combine like terms: 13.872434703 + 11.33333334 = 25.205768043 x = 25.205768043 Simplifying x = 25.205768043Subproblem 2
x + -11.33333334 = -13.872434703 Simplifying x + -11.33333334 = -13.872434703 Reorder the terms: -11.33333334 + x = -13.872434703 Solving -11.33333334 + x = -13.872434703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = -13.872434703 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = -13.872434703 + 11.33333334 x = -13.872434703 + 11.33333334 Combine like terms: -13.872434703 + 11.33333334 = -2.539101363 x = -2.539101363 Simplifying x = -2.539101363Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.205768043, -2.539101363}
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