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Simplifying -12x2 + -3x + 1 = 0 Reorder the terms: 1 + -3x + -12x2 = 0 Solving 1 + -3x + -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 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.25x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.25x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.25x + x2 = 0 + 0.08333333333 0.25x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.25x + x2 = 0.08333333333 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.08333333333 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.08333333333 + 0.015625 Combine like terms: 0.08333333333 + 0.015625 = 0.09895833333 0.015625 + 0.25x + x2 = 0.09895833333 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.09895833333 Calculate the square root of the right side: 0.314576435 Break this problem into two subproblems by setting (x + 0.125) equal to 0.314576435 and -0.314576435.Subproblem 1
x + 0.125 = 0.314576435 Simplifying x + 0.125 = 0.314576435 Reorder the terms: 0.125 + x = 0.314576435 Solving 0.125 + x = 0.314576435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.314576435 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.314576435 + -0.125 x = 0.314576435 + -0.125 Combine like terms: 0.314576435 + -0.125 = 0.189576435 x = 0.189576435 Simplifying x = 0.189576435Subproblem 2
x + 0.125 = -0.314576435 Simplifying x + 0.125 = -0.314576435 Reorder the terms: 0.125 + x = -0.314576435 Solving 0.125 + x = -0.314576435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.314576435 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.314576435 + -0.125 x = -0.314576435 + -0.125 Combine like terms: -0.314576435 + -0.125 = -0.439576435 x = -0.439576435 Simplifying x = -0.439576435Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.189576435, -0.439576435}
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