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Simplifying 5x2 + -34x + 1 = 6x + 1 Reorder the terms: 1 + -34x + 5x2 = 6x + 1 Reorder the terms: 1 + -34x + 5x2 = 1 + 6x Add '-1' to each side of the equation. 1 + -34x + -1 + 5x2 = 1 + -1 + 6x Reorder the terms: 1 + -1 + -34x + 5x2 = 1 + -1 + 6x Combine like terms: 1 + -1 = 0 0 + -34x + 5x2 = 1 + -1 + 6x -34x + 5x2 = 1 + -1 + 6x Combine like terms: 1 + -1 = 0 -34x + 5x2 = 0 + 6x -34x + 5x2 = 6x Solving -34x + 5x2 = 6x Solving for variable 'x'. Reorder the terms: -34x + -6x + 5x2 = 6x + -6x Combine like terms: -34x + -6x = -40x -40x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -40x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-8 + x) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Solution
x = {0, 8}
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