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Simplifying (x + -4)(x + 6) = 11 Reorder the terms: (-4 + x)(x + 6) = 11 Reorder the terms: (-4 + x)(6 + x) = 11 Multiply (-4 + x) * (6 + x) (-4(6 + x) + x(6 + x)) = 11 ((6 * -4 + x * -4) + x(6 + x)) = 11 ((-24 + -4x) + x(6 + x)) = 11 (-24 + -4x + (6 * x + x * x)) = 11 (-24 + -4x + (6x + x2)) = 11 Combine like terms: -4x + 6x = 2x (-24 + 2x + x2) = 11 Solving -24 + 2x + x2 = 11 Solving for variable 'x'. Reorder the terms: -24 + -11 + 2x + x2 = 11 + -11 Combine like terms: -24 + -11 = -35 -35 + 2x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -35 + 2x + x2 = 0 Factor a trinomial. (-7 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-7, 5}
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