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Simplifying 16(x + -4) + -1(x + 3) = (x + 3)(x + -4) Reorder the terms: 16(-4 + x) + -1(x + 3) = (x + 3)(x + -4) (-4 * 16 + x * 16) + -1(x + 3) = (x + 3)(x + -4) (-64 + 16x) + -1(x + 3) = (x + 3)(x + -4) Reorder the terms: -64 + 16x + -1(3 + x) = (x + 3)(x + -4) -64 + 16x + (3 * -1 + x * -1) = (x + 3)(x + -4) -64 + 16x + (-3 + -1x) = (x + 3)(x + -4) Reorder the terms: -64 + -3 + 16x + -1x = (x + 3)(x + -4) Combine like terms: -64 + -3 = -67 -67 + 16x + -1x = (x + 3)(x + -4) Combine like terms: 16x + -1x = 15x -67 + 15x = (x + 3)(x + -4) Reorder the terms: -67 + 15x = (3 + x)(x + -4) Reorder the terms: -67 + 15x = (3 + x)(-4 + x) Multiply (3 + x) * (-4 + x) -67 + 15x = (3(-4 + x) + x(-4 + x)) -67 + 15x = ((-4 * 3 + x * 3) + x(-4 + x)) -67 + 15x = ((-12 + 3x) + x(-4 + x)) -67 + 15x = (-12 + 3x + (-4 * x + x * x)) -67 + 15x = (-12 + 3x + (-4x + x2)) Combine like terms: 3x + -4x = -1x -67 + 15x = (-12 + -1x + x2) Solving -67 + 15x = -12 + -1x + x2 Solving for variable 'x'. Reorder the terms: -67 + 12 + 15x + x + -1x2 = -12 + -1x + x2 + 12 + x + -1x2 Combine like terms: -67 + 12 = -55 -55 + 15x + x + -1x2 = -12 + -1x + x2 + 12 + x + -1x2 Combine like terms: 15x + x = 16x -55 + 16x + -1x2 = -12 + -1x + x2 + 12 + x + -1x2 Reorder the terms: -55 + 16x + -1x2 = -12 + 12 + -1x + x + x2 + -1x2 Combine like terms: -12 + 12 = 0 -55 + 16x + -1x2 = 0 + -1x + x + x2 + -1x2 -55 + 16x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 -55 + 16x + -1x2 = 0 + x2 + -1x2 -55 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -55 + 16x + -1x2 = 0 Factor a trinomial. (-11 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11Subproblem 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 = {11, 5}
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