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Simplifying (x + 4)(x + 4) = (2x + -1)(x + 4) Reorder the terms: (4 + x)(x + 4) = (2x + -1)(x + 4) Reorder the terms: (4 + x)(4 + x) = (2x + -1)(x + 4) Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x)) = (2x + -1)(x + 4) ((4 * 4 + x * 4) + x(4 + x)) = (2x + -1)(x + 4) ((16 + 4x) + x(4 + x)) = (2x + -1)(x + 4) (16 + 4x + (4 * x + x * x)) = (2x + -1)(x + 4) (16 + 4x + (4x + x2)) = (2x + -1)(x + 4) Combine like terms: 4x + 4x = 8x (16 + 8x + x2) = (2x + -1)(x + 4) Reorder the terms: 16 + 8x + x2 = (-1 + 2x)(x + 4) Reorder the terms: 16 + 8x + x2 = (-1 + 2x)(4 + x) Multiply (-1 + 2x) * (4 + x) 16 + 8x + x2 = (-1(4 + x) + 2x * (4 + x)) 16 + 8x + x2 = ((4 * -1 + x * -1) + 2x * (4 + x)) 16 + 8x + x2 = ((-4 + -1x) + 2x * (4 + x)) 16 + 8x + x2 = (-4 + -1x + (4 * 2x + x * 2x)) 16 + 8x + x2 = (-4 + -1x + (8x + 2x2)) Combine like terms: -1x + 8x = 7x 16 + 8x + x2 = (-4 + 7x + 2x2) Solving 16 + 8x + x2 = -4 + 7x + 2x2 Solving for variable 'x'. Reorder the terms: 16 + 4 + 8x + -7x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Combine like terms: 16 + 4 = 20 20 + 8x + -7x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Combine like terms: 8x + -7x = 1x 20 + 1x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Combine like terms: x2 + -2x2 = -1x2 20 + 1x + -1x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Reorder the terms: 20 + 1x + -1x2 = -4 + 4 + 7x + -7x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 20 + 1x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2 20 + 1x + -1x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 20 + 1x + -1x2 = 0 + 2x2 + -2x2 20 + 1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 20 + 1x + -1x2 = 0 Factor a trinomial. (5 + -1x)(4 + x) = 0Subproblem 1
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 = 5Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {5, -4}
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