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Simplifying (5x + 7)(x + 5) = 23 Reorder the terms: (7 + 5x)(x + 5) = 23 Reorder the terms: (7 + 5x)(5 + x) = 23 Multiply (7 + 5x) * (5 + x) (7(5 + x) + 5x * (5 + x)) = 23 ((5 * 7 + x * 7) + 5x * (5 + x)) = 23 ((35 + 7x) + 5x * (5 + x)) = 23 (35 + 7x + (5 * 5x + x * 5x)) = 23 (35 + 7x + (25x + 5x2)) = 23 Combine like terms: 7x + 25x = 32x (35 + 32x + 5x2) = 23 Solving 35 + 32x + 5x2 = 23 Solving for variable 'x'. Reorder the terms: 35 + -23 + 32x + 5x2 = 23 + -23 Combine like terms: 35 + -23 = 12 12 + 32x + 5x2 = 23 + -23 Combine like terms: 23 + -23 = 0 12 + 32x + 5x2 = 0 Factor a trinomial. (6 + x)(2 + 5x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4Solution
x = {-6, -0.4}
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