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Simplifying (2x + 3)(3x + -1) = 11x + 30 Reorder the terms: (3 + 2x)(3x + -1) = 11x + 30 Reorder the terms: (3 + 2x)(-1 + 3x) = 11x + 30 Multiply (3 + 2x) * (-1 + 3x) (3(-1 + 3x) + 2x * (-1 + 3x)) = 11x + 30 ((-1 * 3 + 3x * 3) + 2x * (-1 + 3x)) = 11x + 30 ((-3 + 9x) + 2x * (-1 + 3x)) = 11x + 30 (-3 + 9x + (-1 * 2x + 3x * 2x)) = 11x + 30 (-3 + 9x + (-2x + 6x2)) = 11x + 30 Combine like terms: 9x + -2x = 7x (-3 + 7x + 6x2) = 11x + 30 Reorder the terms: -3 + 7x + 6x2 = 30 + 11x Solving -3 + 7x + 6x2 = 30 + 11x Solving for variable 'x'. Reorder the terms: -3 + -30 + 7x + -11x + 6x2 = 30 + 11x + -30 + -11x Combine like terms: -3 + -30 = -33 -33 + 7x + -11x + 6x2 = 30 + 11x + -30 + -11x Combine like terms: 7x + -11x = -4x -33 + -4x + 6x2 = 30 + 11x + -30 + -11x Reorder the terms: -33 + -4x + 6x2 = 30 + -30 + 11x + -11x Combine like terms: 30 + -30 = 0 -33 + -4x + 6x2 = 0 + 11x + -11x -33 + -4x + 6x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -33 + -4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.5 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -0.6666666667x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -0.6666666667x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -0.6666666667x + x2 = 0 + 5.5 -0.6666666667x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -0.6666666667x + x2 = 5.5 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 5.5 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 5.5 + 0.1111111112 Combine like terms: 5.5 + 0.1111111112 = 5.6111111112 0.1111111112 + -0.6666666667x + x2 = 5.6111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 5.6111111112 Calculate the square root of the right side: 2.368778401 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.368778401 and -2.368778401.Subproblem 1
x + -0.3333333334 = 2.368778401 Simplifying x + -0.3333333334 = 2.368778401 Reorder the terms: -0.3333333334 + x = 2.368778401 Solving -0.3333333334 + x = 2.368778401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 2.368778401 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.368778401 + 0.3333333334 x = 2.368778401 + 0.3333333334 Combine like terms: 2.368778401 + 0.3333333334 = 2.7021117344 x = 2.7021117344 Simplifying x = 2.7021117344Subproblem 2
x + -0.3333333334 = -2.368778401 Simplifying x + -0.3333333334 = -2.368778401 Reorder the terms: -0.3333333334 + x = -2.368778401 Solving -0.3333333334 + x = -2.368778401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -2.368778401 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.368778401 + 0.3333333334 x = -2.368778401 + 0.3333333334 Combine like terms: -2.368778401 + 0.3333333334 = -2.0354450676 x = -2.0354450676 Simplifying x = -2.0354450676Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7021117344, -2.0354450676}
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