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Simplifying (x + 7)(x + 3) = 45 Reorder the terms: (7 + x)(x + 3) = 45 Reorder the terms: (7 + x)(3 + x) = 45 Multiply (7 + x) * (3 + x) (7(3 + x) + x(3 + x)) = 45 ((3 * 7 + x * 7) + x(3 + x)) = 45 ((21 + 7x) + x(3 + x)) = 45 (21 + 7x + (3 * x + x * x)) = 45 (21 + 7x + (3x + x2)) = 45 Combine like terms: 7x + 3x = 10x (21 + 10x + x2) = 45 Solving 21 + 10x + x2 = 45 Solving for variable 'x'. Reorder the terms: 21 + -45 + 10x + x2 = 45 + -45 Combine like terms: 21 + -45 = -24 -24 + 10x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -24 + 10x + x2 = 0 Factor a trinomial. (-12 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 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 = {-12, 2}
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