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Simplifying (x + -3)(x + 2) = 50 Reorder the terms: (-3 + x)(x + 2) = 50 Reorder the terms: (-3 + x)(2 + x) = 50 Multiply (-3 + x) * (2 + x) (-3(2 + x) + x(2 + x)) = 50 ((2 * -3 + x * -3) + x(2 + x)) = 50 ((-6 + -3x) + x(2 + x)) = 50 (-6 + -3x + (2 * x + x * x)) = 50 (-6 + -3x + (2x + x2)) = 50 Combine like terms: -3x + 2x = -1x (-6 + -1x + x2) = 50 Solving -6 + -1x + x2 = 50 Solving for variable 'x'. Reorder the terms: -6 + -50 + -1x + x2 = 50 + -50 Combine like terms: -6 + -50 = -56 -56 + -1x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -56 + -1x + x2 = 0 Factor a trinomial. (-7 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-7, 8}
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