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Simplifying 3x2 + -1x + -27 = 0 Reorder the terms: -27 + -1x + 3x2 = 0 Solving -27 + -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'. -9 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.3333333333x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.3333333333x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.3333333333x + x2 = 0 + 9 -0.3333333333x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.3333333333x + x2 = 9 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 = 9 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 9 + 0.02777777779 Combine like terms: 9 + 0.02777777779 = 9.02777777779 0.02777777779 + -0.3333333333x + x2 = 9.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 9.02777777779 Calculate the square root of the right side: 3.004626063 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 3.004626063 and -3.004626063.Subproblem 1
x + -0.1666666667 = 3.004626063 Simplifying x + -0.1666666667 = 3.004626063 Reorder the terms: -0.1666666667 + x = 3.004626063 Solving -0.1666666667 + x = 3.004626063 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 = 3.004626063 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 3.004626063 + 0.1666666667 x = 3.004626063 + 0.1666666667 Combine like terms: 3.004626063 + 0.1666666667 = 3.1712927297 x = 3.1712927297 Simplifying x = 3.1712927297Subproblem 2
x + -0.1666666667 = -3.004626063 Simplifying x + -0.1666666667 = -3.004626063 Reorder the terms: -0.1666666667 + x = -3.004626063 Solving -0.1666666667 + x = -3.004626063 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 = -3.004626063 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -3.004626063 + 0.1666666667 x = -3.004626063 + 0.1666666667 Combine like terms: -3.004626063 + 0.1666666667 = -2.8379593963 x = -2.8379593963 Simplifying x = -2.8379593963Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1712927297, -2.8379593963}
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