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Simplifying 4x2 + -68 = 5x2 + 21x Reorder the terms: -68 + 4x2 = 5x2 + 21x Reorder the terms: -68 + 4x2 = 21x + 5x2 Solving -68 + 4x2 = 21x + 5x2 Solving for variable 'x'. Reorder the terms: -68 + -21x + 4x2 + -5x2 = 21x + 5x2 + -21x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -68 + -21x + -1x2 = 21x + 5x2 + -21x + -5x2 Reorder the terms: -68 + -21x + -1x2 = 21x + -21x + 5x2 + -5x2 Combine like terms: 21x + -21x = 0 -68 + -21x + -1x2 = 0 + 5x2 + -5x2 -68 + -21x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -68 + -21x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(68 + 21x + x2) = 0 Factor a trinomial. -1((17 + x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Simplifying x = -17Subproblem 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 = {-17, -4}
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