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Simplifying 17x + -4 = (x + 4)(x + 4) Reorder the terms: -4 + 17x = (x + 4)(x + 4) Reorder the terms: -4 + 17x = (4 + x)(x + 4) Reorder the terms: -4 + 17x = (4 + x)(4 + x) Multiply (4 + x) * (4 + x) -4 + 17x = (4(4 + x) + x(4 + x)) -4 + 17x = ((4 * 4 + x * 4) + x(4 + x)) -4 + 17x = ((16 + 4x) + x(4 + x)) -4 + 17x = (16 + 4x + (4 * x + x * x)) -4 + 17x = (16 + 4x + (4x + x2)) Combine like terms: 4x + 4x = 8x -4 + 17x = (16 + 8x + x2) Solving -4 + 17x = 16 + 8x + x2 Solving for variable 'x'. Reorder the terms: -4 + -16 + 17x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: -4 + -16 = -20 -20 + 17x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 17x + -8x = 9x -20 + 9x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Reorder the terms: -20 + 9x + -1x2 = 16 + -16 + 8x + -8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -20 + 9x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -20 + 9x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -20 + 9x + -1x2 = 0 + x2 + -1x2 -20 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -20 + 9x + -1x2 = 0 Factor a trinomial. (-5 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {5, 4}
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