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Simplifying (2x + -3)(3x + 9) = 44 Reorder the terms: (-3 + 2x)(3x + 9) = 44 Reorder the terms: (-3 + 2x)(9 + 3x) = 44 Multiply (-3 + 2x) * (9 + 3x) (-3(9 + 3x) + 2x * (9 + 3x)) = 44 ((9 * -3 + 3x * -3) + 2x * (9 + 3x)) = 44 ((-27 + -9x) + 2x * (9 + 3x)) = 44 (-27 + -9x + (9 * 2x + 3x * 2x)) = 44 (-27 + -9x + (18x + 6x2)) = 44 Combine like terms: -9x + 18x = 9x (-27 + 9x + 6x2) = 44 Solving -27 + 9x + 6x2 = 44 Solving for variable 'x'. Reorder the terms: -27 + -44 + 9x + 6x2 = 44 + -44 Combine like terms: -27 + -44 = -71 -71 + 9x + 6x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -71 + 9x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -11.83333333 + 1.5x + x2 = 0 Move the constant term to the right: Add '11.83333333' to each side of the equation. -11.83333333 + 1.5x + 11.83333333 + x2 = 0 + 11.83333333 Reorder the terms: -11.83333333 + 11.83333333 + 1.5x + x2 = 0 + 11.83333333 Combine like terms: -11.83333333 + 11.83333333 = 0.00000000 0.00000000 + 1.5x + x2 = 0 + 11.83333333 1.5x + x2 = 0 + 11.83333333 Combine like terms: 0 + 11.83333333 = 11.83333333 1.5x + x2 = 11.83333333 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 11.83333333 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 11.83333333 + 0.5625 Combine like terms: 11.83333333 + 0.5625 = 12.39583333 0.5625 + 1.5x + x2 = 12.39583333 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 12.39583333 Calculate the square root of the right side: 3.520771695 Break this problem into two subproblems by setting (x + 0.75) equal to 3.520771695 and -3.520771695.Subproblem 1
x + 0.75 = 3.520771695 Simplifying x + 0.75 = 3.520771695 Reorder the terms: 0.75 + x = 3.520771695 Solving 0.75 + x = 3.520771695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 3.520771695 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.520771695 + -0.75 x = 3.520771695 + -0.75 Combine like terms: 3.520771695 + -0.75 = 2.770771695 x = 2.770771695 Simplifying x = 2.770771695Subproblem 2
x + 0.75 = -3.520771695 Simplifying x + 0.75 = -3.520771695 Reorder the terms: 0.75 + x = -3.520771695 Solving 0.75 + x = -3.520771695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -3.520771695 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.520771695 + -0.75 x = -3.520771695 + -0.75 Combine like terms: -3.520771695 + -0.75 = -4.270771695 x = -4.270771695 Simplifying x = -4.270771695Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.770771695, -4.270771695}
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