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Simplifying 3x2 + -1x + -108 = 0 Reorder the terms: -108 + -1x + 3x2 = 0 Solving -108 + -1x + 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'. -36 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -0.3333333333x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -0.3333333333x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -0.3333333333x + x2 = 0 + 36 -0.3333333333x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -0.3333333333x + x2 = 36 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 36 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 36 + 0.02777777779 Combine like terms: 36 + 0.02777777779 = 36.02777777779 0.02777777779 + -0.3333333333x + x2 = 36.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 36.02777777779 Calculate the square root of the right side: 6.002314368 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 6.002314368 and -6.002314368.Subproblem 1
x + -0.1666666667 = 6.002314368 Simplifying x + -0.1666666667 = 6.002314368 Reorder the terms: -0.1666666667 + x = 6.002314368 Solving -0.1666666667 + x = 6.002314368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 6.002314368 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 6.002314368 + 0.1666666667 x = 6.002314368 + 0.1666666667 Combine like terms: 6.002314368 + 0.1666666667 = 6.1689810347 x = 6.1689810347 Simplifying x = 6.1689810347Subproblem 2
x + -0.1666666667 = -6.002314368 Simplifying x + -0.1666666667 = -6.002314368 Reorder the terms: -0.1666666667 + x = -6.002314368 Solving -0.1666666667 + x = -6.002314368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -6.002314368 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -6.002314368 + 0.1666666667 x = -6.002314368 + 0.1666666667 Combine like terms: -6.002314368 + 0.1666666667 = -5.8356477013 x = -5.8356477013 Simplifying x = -5.8356477013Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.1689810347, -5.8356477013}
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