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Simplifying 6x(2x + -1) = 5 + -5x Reorder the terms: 6x(-1 + 2x) = 5 + -5x (-1 * 6x + 2x * 6x) = 5 + -5x (-6x + 12x2) = 5 + -5x Solving -6x + 12x2 = 5 + -5x Solving for variable 'x'. Reorder the terms: -5 + -6x + 5x + 12x2 = 5 + -5x + -5 + 5x Combine like terms: -6x + 5x = -1x -5 + -1x + 12x2 = 5 + -5x + -5 + 5x Reorder the terms: -5 + -1x + 12x2 = 5 + -5 + -5x + 5x Combine like terms: 5 + -5 = 0 -5 + -1x + 12x2 = 0 + -5x + 5x -5 + -1x + 12x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -5 + -1x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.08333333333x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.08333333333x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.08333333333x + x2 = 0 + 0.4166666667 -0.08333333333x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.08333333333x + x2 = 0.4166666667 The x term is -0.08333333333x. Take half its coefficient (-0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. -0.08333333333x + 0.001736111111 + x2 = 0.4166666667 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333x + x2 = 0.4166666667 + 0.001736111111 Combine like terms: 0.4166666667 + 0.001736111111 = 0.418402777811 0.001736111111 + -0.08333333333x + x2 = 0.418402777811 Factor a perfect square on the left side: (x + -0.04166666667)(x + -0.04166666667) = 0.418402777811 Calculate the square root of the right side: 0.646840612 Break this problem into two subproblems by setting (x + -0.04166666667) equal to 0.646840612 and -0.646840612.Subproblem 1
x + -0.04166666667 = 0.646840612 Simplifying x + -0.04166666667 = 0.646840612 Reorder the terms: -0.04166666667 + x = 0.646840612 Solving -0.04166666667 + x = 0.646840612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = 0.646840612 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 0.646840612 + 0.04166666667 x = 0.646840612 + 0.04166666667 Combine like terms: 0.646840612 + 0.04166666667 = 0.68850727867 x = 0.68850727867 Simplifying x = 0.68850727867Subproblem 2
x + -0.04166666667 = -0.646840612 Simplifying x + -0.04166666667 = -0.646840612 Reorder the terms: -0.04166666667 + x = -0.646840612 Solving -0.04166666667 + x = -0.646840612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = -0.646840612 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -0.646840612 + 0.04166666667 x = -0.646840612 + 0.04166666667 Combine like terms: -0.646840612 + 0.04166666667 = -0.60517394533 x = -0.60517394533 Simplifying x = -0.60517394533Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.68850727867, -0.60517394533}
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