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Simplifying (2x + -4)(3x + -9) = 1 Reorder the terms: (-4 + 2x)(3x + -9) = 1 Reorder the terms: (-4 + 2x)(-9 + 3x) = 1 Multiply (-4 + 2x) * (-9 + 3x) (-4(-9 + 3x) + 2x * (-9 + 3x)) = 1 ((-9 * -4 + 3x * -4) + 2x * (-9 + 3x)) = 1 ((36 + -12x) + 2x * (-9 + 3x)) = 1 (36 + -12x + (-9 * 2x + 3x * 2x)) = 1 (36 + -12x + (-18x + 6x2)) = 1 Combine like terms: -12x + -18x = -30x (36 + -30x + 6x2) = 1 Solving 36 + -30x + 6x2 = 1 Solving for variable 'x'. Reorder the terms: 36 + -1 + -30x + 6x2 = 1 + -1 Combine like terms: 36 + -1 = 35 35 + -30x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 35 + -30x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 5.833333333 + -5x + x2 = 0 Move the constant term to the right: Add '-5.833333333' to each side of the equation. 5.833333333 + -5x + -5.833333333 + x2 = 0 + -5.833333333 Reorder the terms: 5.833333333 + -5.833333333 + -5x + x2 = 0 + -5.833333333 Combine like terms: 5.833333333 + -5.833333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + -5.833333333 -5x + x2 = 0 + -5.833333333 Combine like terms: 0 + -5.833333333 = -5.833333333 -5x + x2 = -5.833333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -5.833333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -5.833333333 + 6.25 Combine like terms: -5.833333333 + 6.25 = 0.416666667 6.25 + -5x + x2 = 0.416666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 0.416666667 Calculate the square root of the right side: 0.645497225 Break this problem into two subproblems by setting (x + -2.5) equal to 0.645497225 and -0.645497225.Subproblem 1
x + -2.5 = 0.645497225 Simplifying x + -2.5 = 0.645497225 Reorder the terms: -2.5 + x = 0.645497225 Solving -2.5 + x = 0.645497225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 0.645497225 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 0.645497225 + 2.5 x = 0.645497225 + 2.5 Combine like terms: 0.645497225 + 2.5 = 3.145497225 x = 3.145497225 Simplifying x = 3.145497225Subproblem 2
x + -2.5 = -0.645497225 Simplifying x + -2.5 = -0.645497225 Reorder the terms: -2.5 + x = -0.645497225 Solving -2.5 + x = -0.645497225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -0.645497225 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -0.645497225 + 2.5 x = -0.645497225 + 2.5 Combine like terms: -0.645497225 + 2.5 = 1.854502775 x = 1.854502775 Simplifying x = 1.854502775Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.145497225, 1.854502775}
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