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Simplifying 3x2 + -1x + -12 = 0 Reorder the terms: -12 + -1x + 3x2 = 0 Solving -12 + -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'. -4 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.3333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.3333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.3333333333x + x2 = 0 + 4 -0.3333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.3333333333x + x2 = 4 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 = 4 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 4 + 0.02777777779 Combine like terms: 4 + 0.02777777779 = 4.02777777779 0.02777777779 + -0.3333333333x + x2 = 4.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 4.02777777779 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 2.00693243 and -2.00693243.Subproblem 1
x + -0.1666666667 = 2.00693243 Simplifying x + -0.1666666667 = 2.00693243 Reorder the terms: -0.1666666667 + x = 2.00693243 Solving -0.1666666667 + x = 2.00693243 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 = 2.00693243 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 2.00693243 + 0.1666666667 x = 2.00693243 + 0.1666666667 Combine like terms: 2.00693243 + 0.1666666667 = 2.1735990967 x = 2.1735990967 Simplifying x = 2.1735990967Subproblem 2
x + -0.1666666667 = -2.00693243 Simplifying x + -0.1666666667 = -2.00693243 Reorder the terms: -0.1666666667 + x = -2.00693243 Solving -0.1666666667 + x = -2.00693243 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 = -2.00693243 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -2.00693243 + 0.1666666667 x = -2.00693243 + 0.1666666667 Combine like terms: -2.00693243 + 0.1666666667 = -1.8402657633 x = -1.8402657633 Simplifying x = -1.8402657633Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1735990967, -1.8402657633}
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