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Simplifying 4x + 1 = 4x2 + -16x + 17 Reorder the terms: 1 + 4x = 4x2 + -16x + 17 Reorder the terms: 1 + 4x = 17 + -16x + 4x2 Solving 1 + 4x = 17 + -16x + 4x2 Solving for variable 'x'. Reorder the terms: 1 + -17 + 4x + 16x + -4x2 = 17 + -16x + 4x2 + -17 + 16x + -4x2 Combine like terms: 1 + -17 = -16 -16 + 4x + 16x + -4x2 = 17 + -16x + 4x2 + -17 + 16x + -4x2 Combine like terms: 4x + 16x = 20x -16 + 20x + -4x2 = 17 + -16x + 4x2 + -17 + 16x + -4x2 Reorder the terms: -16 + 20x + -4x2 = 17 + -17 + -16x + 16x + 4x2 + -4x2 Combine like terms: 17 + -17 = 0 -16 + 20x + -4x2 = 0 + -16x + 16x + 4x2 + -4x2 -16 + 20x + -4x2 = -16x + 16x + 4x2 + -4x2 Combine like terms: -16x + 16x = 0 -16 + 20x + -4x2 = 0 + 4x2 + -4x2 -16 + 20x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -16 + 20x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 5x + -1x2) = 0 Factor a trinomial. 4((-4 + x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 = 4Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {4, 1}
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