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Simplifying (2x + -1)(3x + 1) = 12 Reorder the terms: (-1 + 2x)(3x + 1) = 12 Reorder the terms: (-1 + 2x)(1 + 3x) = 12 Multiply (-1 + 2x) * (1 + 3x) (-1(1 + 3x) + 2x * (1 + 3x)) = 12 ((1 * -1 + 3x * -1) + 2x * (1 + 3x)) = 12 ((-1 + -3x) + 2x * (1 + 3x)) = 12 (-1 + -3x + (1 * 2x + 3x * 2x)) = 12 (-1 + -3x + (2x + 6x2)) = 12 Combine like terms: -3x + 2x = -1x (-1 + -1x + 6x2) = 12 Solving -1 + -1x + 6x2 = 12 Solving for variable 'x'. Reorder the terms: -1 + -12 + -1x + 6x2 = 12 + -12 Combine like terms: -1 + -12 = -13 -13 + -1x + 6x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -13 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + -0.1666666667x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + -0.1666666667x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 2.166666667 -0.1666666667x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 -0.1666666667x + x2 = 2.166666667 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 2.166666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 2.166666667 + 0.006944444447 Combine like terms: 2.166666667 + 0.006944444447 = 2.173611111447 0.006944444447 + -0.1666666667x + x2 = 2.173611111447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 2.173611111447 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.474317168 and -1.474317168.Subproblem 1
x + -0.08333333335 = 1.474317168 Simplifying x + -0.08333333335 = 1.474317168 Reorder the terms: -0.08333333335 + x = 1.474317168 Solving -0.08333333335 + x = 1.474317168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 1.474317168 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.474317168 + 0.08333333335 x = 1.474317168 + 0.08333333335 Combine like terms: 1.474317168 + 0.08333333335 = 1.55765050135 x = 1.55765050135 Simplifying x = 1.55765050135Subproblem 2
x + -0.08333333335 = -1.474317168 Simplifying x + -0.08333333335 = -1.474317168 Reorder the terms: -0.08333333335 + x = -1.474317168 Solving -0.08333333335 + x = -1.474317168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -1.474317168 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.474317168 + 0.08333333335 x = -1.474317168 + 0.08333333335 Combine like terms: -1.474317168 + 0.08333333335 = -1.39098383465 x = -1.39098383465 Simplifying x = -1.39098383465Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.55765050135, -1.39098383465}
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