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Simplifying (x + 7)(x + -4) = 26 Reorder the terms: (7 + x)(x + -4) = 26 Reorder the terms: (7 + x)(-4 + x) = 26 Multiply (7 + x) * (-4 + x) (7(-4 + x) + x(-4 + x)) = 26 ((-4 * 7 + x * 7) + x(-4 + x)) = 26 ((-28 + 7x) + x(-4 + x)) = 26 (-28 + 7x + (-4 * x + x * x)) = 26 (-28 + 7x + (-4x + x2)) = 26 Combine like terms: 7x + -4x = 3x (-28 + 3x + x2) = 26 Solving -28 + 3x + x2 = 26 Solving for variable 'x'. Reorder the terms: -28 + -26 + 3x + x2 = 26 + -26 Combine like terms: -28 + -26 = -54 -54 + 3x + x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -54 + 3x + x2 = 0 Factor a trinomial. (-9 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-9, 6}
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