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Simplifying (3x + 11)(x + 7) = 625 Reorder the terms: (11 + 3x)(x + 7) = 625 Reorder the terms: (11 + 3x)(7 + x) = 625 Multiply (11 + 3x) * (7 + x) (11(7 + x) + 3x * (7 + x)) = 625 ((7 * 11 + x * 11) + 3x * (7 + x)) = 625 ((77 + 11x) + 3x * (7 + x)) = 625 (77 + 11x + (7 * 3x + x * 3x)) = 625 (77 + 11x + (21x + 3x2)) = 625 Combine like terms: 11x + 21x = 32x (77 + 32x + 3x2) = 625 Solving 77 + 32x + 3x2 = 625 Solving for variable 'x'. Reorder the terms: 77 + -625 + 32x + 3x2 = 625 + -625 Combine like terms: 77 + -625 = -548 -548 + 32x + 3x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -548 + 32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -182.6666667 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '182.6666667' to each side of the equation. -182.6666667 + 10.66666667x + 182.6666667 + x2 = 0 + 182.6666667 Reorder the terms: -182.6666667 + 182.6666667 + 10.66666667x + x2 = 0 + 182.6666667 Combine like terms: -182.6666667 + 182.6666667 = 0.0000000 0.0000000 + 10.66666667x + x2 = 0 + 182.6666667 10.66666667x + x2 = 0 + 182.6666667 Combine like terms: 0 + 182.6666667 = 182.6666667 10.66666667x + x2 = 182.6666667 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = 182.6666667 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = 182.6666667 + 28.44444446 Combine like terms: 182.6666667 + 28.44444446 = 211.11111116 28.44444446 + 10.66666667x + x2 = 211.11111116 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 211.11111116 Calculate the square root of the right side: 14.529663147 Break this problem into two subproblems by setting (x + 5.333333335) equal to 14.529663147 and -14.529663147.Subproblem 1
x + 5.333333335 = 14.529663147 Simplifying x + 5.333333335 = 14.529663147 Reorder the terms: 5.333333335 + x = 14.529663147 Solving 5.333333335 + x = 14.529663147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 14.529663147 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 14.529663147 + -5.333333335 x = 14.529663147 + -5.333333335 Combine like terms: 14.529663147 + -5.333333335 = 9.196329812 x = 9.196329812 Simplifying x = 9.196329812Subproblem 2
x + 5.333333335 = -14.529663147 Simplifying x + 5.333333335 = -14.529663147 Reorder the terms: 5.333333335 + x = -14.529663147 Solving 5.333333335 + x = -14.529663147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -14.529663147 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -14.529663147 + -5.333333335 x = -14.529663147 + -5.333333335 Combine like terms: -14.529663147 + -5.333333335 = -19.862996482 x = -19.862996482 Simplifying x = -19.862996482Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.196329812, -19.862996482}
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