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Simplifying (2x + -1)(3x + 2) = 170 Reorder the terms: (-1 + 2x)(3x + 2) = 170 Reorder the terms: (-1 + 2x)(2 + 3x) = 170 Multiply (-1 + 2x) * (2 + 3x) (-1(2 + 3x) + 2x * (2 + 3x)) = 170 ((2 * -1 + 3x * -1) + 2x * (2 + 3x)) = 170 ((-2 + -3x) + 2x * (2 + 3x)) = 170 (-2 + -3x + (2 * 2x + 3x * 2x)) = 170 (-2 + -3x + (4x + 6x2)) = 170 Combine like terms: -3x + 4x = 1x (-2 + 1x + 6x2) = 170 Solving -2 + 1x + 6x2 = 170 Solving for variable 'x'. Reorder the terms: -2 + -170 + 1x + 6x2 = 170 + -170 Combine like terms: -2 + -170 = -172 -172 + 1x + 6x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -172 + 1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -28.66666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '28.66666667' to each side of the equation. -28.66666667 + 0.1666666667x + 28.66666667 + x2 = 0 + 28.66666667 Reorder the terms: -28.66666667 + 28.66666667 + 0.1666666667x + x2 = 0 + 28.66666667 Combine like terms: -28.66666667 + 28.66666667 = 0.00000000 0.00000000 + 0.1666666667x + x2 = 0 + 28.66666667 0.1666666667x + x2 = 0 + 28.66666667 Combine like terms: 0 + 28.66666667 = 28.66666667 0.1666666667x + x2 = 28.66666667 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 = 28.66666667 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 28.66666667 + 0.006944444447 Combine like terms: 28.66666667 + 0.006944444447 = 28.673611114447 0.006944444447 + 0.1666666667x + x2 = 28.673611114447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 28.673611114447 Calculate the square root of the right side: 5.354774609 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 5.354774609 and -5.354774609.Subproblem 1
x + 0.08333333335 = 5.354774609 Simplifying x + 0.08333333335 = 5.354774609 Reorder the terms: 0.08333333335 + x = 5.354774609 Solving 0.08333333335 + x = 5.354774609 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 = 5.354774609 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 5.354774609 + -0.08333333335 x = 5.354774609 + -0.08333333335 Combine like terms: 5.354774609 + -0.08333333335 = 5.27144127565 x = 5.27144127565 Simplifying x = 5.27144127565Subproblem 2
x + 0.08333333335 = -5.354774609 Simplifying x + 0.08333333335 = -5.354774609 Reorder the terms: 0.08333333335 + x = -5.354774609 Solving 0.08333333335 + x = -5.354774609 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 = -5.354774609 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -5.354774609 + -0.08333333335 x = -5.354774609 + -0.08333333335 Combine like terms: -5.354774609 + -0.08333333335 = -5.43810794235 x = -5.43810794235 Simplifying x = -5.43810794235Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.27144127565, -5.43810794235}
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