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Simplifying 0 = -16x2 + -22x + 344 Reorder the terms: 0 = 344 + -22x + -16x2 Solving 0 = 344 + -22x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -344 = -344 -344 + 22x + 16x2 = 344 + -22x + -16x2 + -344 + 22x + 16x2 Reorder the terms: -344 + 22x + 16x2 = 344 + -344 + -22x + 22x + -16x2 + 16x2 Combine like terms: 344 + -344 = 0 -344 + 22x + 16x2 = 0 + -22x + 22x + -16x2 + 16x2 -344 + 22x + 16x2 = -22x + 22x + -16x2 + 16x2 Combine like terms: -22x + 22x = 0 -344 + 22x + 16x2 = 0 + -16x2 + 16x2 -344 + 22x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -344 + 22x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-172 + 11x + 8x2) = 0 Factor a trinomial. 2((-43 + -8x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-43 + -8x)' equal to zero and attempt to solve: Simplifying -43 + -8x = 0 Solving -43 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + -8x = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -8x = 0 + 43 -8x = 0 + 43 Combine like terms: 0 + 43 = 43 -8x = 43 Divide each side by '-8'. x = -5.375 Simplifying x = -5.375Subproblem 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 = {-5.375, 4}
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