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Simplifying 12x2 + -24x + 1 = 0 Reorder the terms: 1 + -24x + 12x2 = 0 Solving 1 + -24x + 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 + -2x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -2x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -2x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -2x + x2 = 0 + -0.08333333333 -2x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -2x + x2 = -0.08333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.08333333333 + 1 Reorder the terms: 1 + -2x + x2 = -0.08333333333 + 1 Combine like terms: -0.08333333333 + 1 = 0.91666666667 1 + -2x + x2 = 0.91666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.91666666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + -1) equal to 0.957427108 and -0.957427108.Subproblem 1
x + -1 = 0.957427108 Simplifying x + -1 = 0.957427108 Reorder the terms: -1 + x = 0.957427108 Solving -1 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.957427108 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.957427108 + 1 x = 0.957427108 + 1 Combine like terms: 0.957427108 + 1 = 1.957427108 x = 1.957427108 Simplifying x = 1.957427108Subproblem 2
x + -1 = -0.957427108 Simplifying x + -1 = -0.957427108 Reorder the terms: -1 + x = -0.957427108 Solving -1 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.957427108 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.957427108 + 1 x = -0.957427108 + 1 Combine like terms: -0.957427108 + 1 = 0.042572892 x = 0.042572892 Simplifying x = 0.042572892Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.957427108, 0.042572892}
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