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Simplifying (7x + 4)(3x + 9) = 133 Reorder the terms: (4 + 7x)(3x + 9) = 133 Reorder the terms: (4 + 7x)(9 + 3x) = 133 Multiply (4 + 7x) * (9 + 3x) (4(9 + 3x) + 7x * (9 + 3x)) = 133 ((9 * 4 + 3x * 4) + 7x * (9 + 3x)) = 133 ((36 + 12x) + 7x * (9 + 3x)) = 133 (36 + 12x + (9 * 7x + 3x * 7x)) = 133 (36 + 12x + (63x + 21x2)) = 133 Combine like terms: 12x + 63x = 75x (36 + 75x + 21x2) = 133 Solving 36 + 75x + 21x2 = 133 Solving for variable 'x'. Reorder the terms: 36 + -133 + 75x + 21x2 = 133 + -133 Combine like terms: 36 + -133 = -97 -97 + 75x + 21x2 = 133 + -133 Combine like terms: 133 + -133 = 0 -97 + 75x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -4.619047619 + 3.571428571x + x2 = 0 Move the constant term to the right: Add '4.619047619' to each side of the equation. -4.619047619 + 3.571428571x + 4.619047619 + x2 = 0 + 4.619047619 Reorder the terms: -4.619047619 + 4.619047619 + 3.571428571x + x2 = 0 + 4.619047619 Combine like terms: -4.619047619 + 4.619047619 = 0.000000000 0.000000000 + 3.571428571x + x2 = 0 + 4.619047619 3.571428571x + x2 = 0 + 4.619047619 Combine like terms: 0 + 4.619047619 = 4.619047619 3.571428571x + x2 = 4.619047619 The x term is 3.571428571x. Take half its coefficient (1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. 3.571428571x + 3.188775511 + x2 = 4.619047619 + 3.188775511 Reorder the terms: 3.188775511 + 3.571428571x + x2 = 4.619047619 + 3.188775511 Combine like terms: 4.619047619 + 3.188775511 = 7.80782313 3.188775511 + 3.571428571x + x2 = 7.80782313 Factor a perfect square on the left side: (x + 1.785714286)(x + 1.785714286) = 7.80782313 Calculate the square root of the right side: 2.794248223 Break this problem into two subproblems by setting (x + 1.785714286) equal to 2.794248223 and -2.794248223.Subproblem 1
x + 1.785714286 = 2.794248223 Simplifying x + 1.785714286 = 2.794248223 Reorder the terms: 1.785714286 + x = 2.794248223 Solving 1.785714286 + x = 2.794248223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = 2.794248223 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = 2.794248223 + -1.785714286 x = 2.794248223 + -1.785714286 Combine like terms: 2.794248223 + -1.785714286 = 1.008533937 x = 1.008533937 Simplifying x = 1.008533937Subproblem 2
x + 1.785714286 = -2.794248223 Simplifying x + 1.785714286 = -2.794248223 Reorder the terms: 1.785714286 + x = -2.794248223 Solving 1.785714286 + x = -2.794248223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = -2.794248223 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = -2.794248223 + -1.785714286 x = -2.794248223 + -1.785714286 Combine like terms: -2.794248223 + -1.785714286 = -4.579962509 x = -4.579962509 Simplifying x = -4.579962509Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.008533937, -4.579962509}
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