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Simplifying 30x2 + -1x + -12 = 0 Reorder the terms: -12 + -1x + 30x2 = 0 Solving -12 + -1x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.4 + -0.03333333333x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.03333333333x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.03333333333x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.03333333333x + x2 = 0 + 0.4 -0.03333333333x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.03333333333x + x2 = 0.4 The x term is -0.03333333333x. Take half its coefficient (-0.01666666667). Square it (0.0002777777779) and add it to both sides. Add '0.0002777777779' to each side of the equation. -0.03333333333x + 0.0002777777779 + x2 = 0.4 + 0.0002777777779 Reorder the terms: 0.0002777777779 + -0.03333333333x + x2 = 0.4 + 0.0002777777779 Combine like terms: 0.4 + 0.0002777777779 = 0.4002777777779 0.0002777777779 + -0.03333333333x + x2 = 0.4002777777779 Factor a perfect square on the left side: (x + -0.01666666667)(x + -0.01666666667) = 0.4002777777779 Calculate the square root of the right side: 0.632675097 Break this problem into two subproblems by setting (x + -0.01666666667) equal to 0.632675097 and -0.632675097.Subproblem 1
x + -0.01666666667 = 0.632675097 Simplifying x + -0.01666666667 = 0.632675097 Reorder the terms: -0.01666666667 + x = 0.632675097 Solving -0.01666666667 + x = 0.632675097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01666666667' to each side of the equation. -0.01666666667 + 0.01666666667 + x = 0.632675097 + 0.01666666667 Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000 0.00000000000 + x = 0.632675097 + 0.01666666667 x = 0.632675097 + 0.01666666667 Combine like terms: 0.632675097 + 0.01666666667 = 0.64934176367 x = 0.64934176367 Simplifying x = 0.64934176367Subproblem 2
x + -0.01666666667 = -0.632675097 Simplifying x + -0.01666666667 = -0.632675097 Reorder the terms: -0.01666666667 + x = -0.632675097 Solving -0.01666666667 + x = -0.632675097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01666666667' to each side of the equation. -0.01666666667 + 0.01666666667 + x = -0.632675097 + 0.01666666667 Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000 0.00000000000 + x = -0.632675097 + 0.01666666667 x = -0.632675097 + 0.01666666667 Combine like terms: -0.632675097 + 0.01666666667 = -0.61600843033 x = -0.61600843033 Simplifying x = -0.61600843033Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.64934176367, -0.61600843033}
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