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Simplifying (x + 3)(x + 5) = 35 Reorder the terms: (3 + x)(x + 5) = 35 Reorder the terms: (3 + x)(5 + x) = 35 Multiply (3 + x) * (5 + x) (3(5 + x) + x(5 + x)) = 35 ((5 * 3 + x * 3) + x(5 + x)) = 35 ((15 + 3x) + x(5 + x)) = 35 (15 + 3x + (5 * x + x * x)) = 35 (15 + 3x + (5x + x2)) = 35 Combine like terms: 3x + 5x = 8x (15 + 8x + x2) = 35 Solving 15 + 8x + x2 = 35 Solving for variable 'x'. Reorder the terms: 15 + -35 + 8x + x2 = 35 + -35 Combine like terms: 15 + -35 = -20 -20 + 8x + x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -20 + 8x + x2 = 0 Factor a trinomial. (-10 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-10, 2}
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