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Simplifying (3x + -1)(2x + 3) = 6x Reorder the terms: (-1 + 3x)(2x + 3) = 6x Reorder the terms: (-1 + 3x)(3 + 2x) = 6x Multiply (-1 + 3x) * (3 + 2x) (-1(3 + 2x) + 3x * (3 + 2x)) = 6x ((3 * -1 + 2x * -1) + 3x * (3 + 2x)) = 6x ((-3 + -2x) + 3x * (3 + 2x)) = 6x (-3 + -2x + (3 * 3x + 2x * 3x)) = 6x (-3 + -2x + (9x + 6x2)) = 6x Combine like terms: -2x + 9x = 7x (-3 + 7x + 6x2) = 6x Solving -3 + 7x + 6x2 = 6x Solving for variable 'x'. Reorder the terms: -3 + 7x + -6x + 6x2 = 6x + -6x Combine like terms: 7x + -6x = 1x -3 + 1x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 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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