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Simplifying 0 = 12x2 + -3x + -4x + -1 Reorder the terms: 0 = -1 + -3x + -4x + 12x2 Combine like terms: -3x + -4x = -7x 0 = -1 + -7x + 12x2 Solving 0 = -1 + -7x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 1 = 1 1 + 7x + -12x2 = -1 + -7x + 12x2 + 1 + 7x + -12x2 Reorder the terms: 1 + 7x + -12x2 = -1 + 1 + -7x + 7x + 12x2 + -12x2 Combine like terms: -1 + 1 = 0 1 + 7x + -12x2 = 0 + -7x + 7x + 12x2 + -12x2 1 + 7x + -12x2 = -7x + 7x + 12x2 + -12x2 Combine like terms: -7x + 7x = 0 1 + 7x + -12x2 = 0 + 12x2 + -12x2 1 + 7x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 1 + 7x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.08333333333 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -0.5833333333x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -0.5833333333x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -0.5833333333x + x2 = 0 + 0.08333333333 -0.5833333333x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -0.5833333333x + x2 = 0.08333333333 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 0.08333333333 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 0.08333333333 + 0.08506944446 Combine like terms: 0.08333333333 + 0.08506944446 = 0.16840277779 0.08506944446 + -0.5833333333x + x2 = 0.16840277779 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.16840277779 Calculate the square root of the right side: 0.410369075 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.410369075 and -0.410369075.Subproblem 1
x + -0.2916666667 = 0.410369075 Simplifying x + -0.2916666667 = 0.410369075 Reorder the terms: -0.2916666667 + x = 0.410369075 Solving -0.2916666667 + x = 0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.410369075 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.410369075 + 0.2916666667 x = 0.410369075 + 0.2916666667 Combine like terms: 0.410369075 + 0.2916666667 = 0.7020357417 x = 0.7020357417 Simplifying x = 0.7020357417Subproblem 2
x + -0.2916666667 = -0.410369075 Simplifying x + -0.2916666667 = -0.410369075 Reorder the terms: -0.2916666667 + x = -0.410369075 Solving -0.2916666667 + x = -0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.410369075 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.410369075 + 0.2916666667 x = -0.410369075 + 0.2916666667 Combine like terms: -0.410369075 + 0.2916666667 = -0.1187024083 x = -0.1187024083 Simplifying x = -0.1187024083Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7020357417, -0.1187024083}
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