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Simplifying (4x + 12x2 + -27) = 0 Reorder the terms: (-27 + 4x + 12x2) = 0 Remove parenthesis around (-27 + 4x + 12x2) -27 + 4x + 12x2 = 0 Solving -27 + 4x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.25 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.3333333333x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.3333333333x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.3333333333x + x2 = 0 + 2.25 0.3333333333x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.3333333333x + x2 = 2.25 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 = 2.25 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 2.25 + 0.02777777779 Combine like terms: 2.25 + 0.02777777779 = 2.27777777779 0.02777777779 + 0.3333333333x + x2 = 2.27777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 2.27777777779 Calculate the square root of the right side: 1.509230856 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.509230856 and -1.509230856.Subproblem 1
x + 0.1666666667 = 1.509230856 Simplifying x + 0.1666666667 = 1.509230856 Reorder the terms: 0.1666666667 + x = 1.509230856 Solving 0.1666666667 + x = 1.509230856 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 = 1.509230856 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.509230856 + -0.1666666667 x = 1.509230856 + -0.1666666667 Combine like terms: 1.509230856 + -0.1666666667 = 1.3425641893 x = 1.3425641893 Simplifying x = 1.3425641893Subproblem 2
x + 0.1666666667 = -1.509230856 Simplifying x + 0.1666666667 = -1.509230856 Reorder the terms: 0.1666666667 + x = -1.509230856 Solving 0.1666666667 + x = -1.509230856 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 = -1.509230856 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.509230856 + -0.1666666667 x = -1.509230856 + -0.1666666667 Combine like terms: -1.509230856 + -0.1666666667 = -1.6758975227 x = -1.6758975227 Simplifying x = -1.6758975227Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3425641893, -1.6758975227}
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