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Simplifying 12x2 + -6x + -1 = 0 Reorder the terms: -1 + -6x + 12x2 = 0 Solving -1 + -6x + 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'. -0.08333333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -0.5x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -0.5x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -0.5x + x2 = 0 + 0.08333333333 -0.5x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -0.5x + x2 = 0.08333333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.08333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.08333333333 + 0.0625 Combine like terms: 0.08333333333 + 0.0625 = 0.14583333333 0.0625 + -0.5x + x2 = 0.14583333333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.14583333333 Calculate the square root of the right side: 0.381881308 Break this problem into two subproblems by setting (x + -0.25) equal to 0.381881308 and -0.381881308.Subproblem 1
x + -0.25 = 0.381881308 Simplifying x + -0.25 = 0.381881308 Reorder the terms: -0.25 + x = 0.381881308 Solving -0.25 + x = 0.381881308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.381881308 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.381881308 + 0.25 x = 0.381881308 + 0.25 Combine like terms: 0.381881308 + 0.25 = 0.631881308 x = 0.631881308 Simplifying x = 0.631881308Subproblem 2
x + -0.25 = -0.381881308 Simplifying x + -0.25 = -0.381881308 Reorder the terms: -0.25 + x = -0.381881308 Solving -0.25 + x = -0.381881308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.381881308 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.381881308 + 0.25 x = -0.381881308 + 0.25 Combine like terms: -0.381881308 + 0.25 = -0.131881308 x = -0.131881308 Simplifying x = -0.131881308Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.631881308, -0.131881308}
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