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Simplifying (3x + -1)(2x + 1) = 2 Reorder the terms: (-1 + 3x)(2x + 1) = 2 Reorder the terms: (-1 + 3x)(1 + 2x) = 2 Multiply (-1 + 3x) * (1 + 2x) (-1(1 + 2x) + 3x * (1 + 2x)) = 2 ((1 * -1 + 2x * -1) + 3x * (1 + 2x)) = 2 ((-1 + -2x) + 3x * (1 + 2x)) = 2 (-1 + -2x + (1 * 3x + 2x * 3x)) = 2 (-1 + -2x + (3x + 6x2)) = 2 Combine like terms: -2x + 3x = 1x (-1 + 1x + 6x2) = 2 Solving -1 + 1x + 6x2 = 2 Solving for variable 'x'. Reorder the terms: -1 + -2 + 1x + 6x2 = 2 + -2 Combine like terms: -1 + -2 = -3 -3 + 1x + 6x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -3 + 1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.1666666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.1666666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.1666666667x + x2 = 0 + 0.5 0.1666666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.1666666667x + x2 = 0.5 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 = 0.5 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 0.5 + 0.006944444447 Combine like terms: 0.5 + 0.006944444447 = 0.506944444447 0.006944444447 + 0.1666666667x + x2 = 0.506944444447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 0.506944444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 0.712000312 and -0.712000312.Subproblem 1
x + 0.08333333335 = 0.712000312 Simplifying x + 0.08333333335 = 0.712000312 Reorder the terms: 0.08333333335 + x = 0.712000312 Solving 0.08333333335 + x = 0.712000312 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 = 0.712000312 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 0.712000312 + -0.08333333335 x = 0.712000312 + -0.08333333335 Combine like terms: 0.712000312 + -0.08333333335 = 0.62866697865 x = 0.62866697865 Simplifying x = 0.62866697865Subproblem 2
x + 0.08333333335 = -0.712000312 Simplifying x + 0.08333333335 = -0.712000312 Reorder the terms: 0.08333333335 + x = -0.712000312 Solving 0.08333333335 + x = -0.712000312 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 = -0.712000312 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -0.712000312 + -0.08333333335 x = -0.712000312 + -0.08333333335 Combine like terms: -0.712000312 + -0.08333333335 = -0.79533364535 x = -0.79533364535 Simplifying x = -0.79533364535Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.62866697865, -0.79533364535}
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