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Simplifying 1 = 5x2 + -35x + 31 Reorder the terms: 1 = 31 + -35x + 5x2 Solving 1 = 31 + -35x + 5x2 Solving for variable 'x'. Combine like terms: 1 + -31 = -30 -30 + 35x + -5x2 = 31 + -35x + 5x2 + -31 + 35x + -5x2 Reorder the terms: -30 + 35x + -5x2 = 31 + -31 + -35x + 35x + 5x2 + -5x2 Combine like terms: 31 + -31 = 0 -30 + 35x + -5x2 = 0 + -35x + 35x + 5x2 + -5x2 -30 + 35x + -5x2 = -35x + 35x + 5x2 + -5x2 Combine like terms: -35x + 35x = 0 -30 + 35x + -5x2 = 0 + 5x2 + -5x2 -30 + 35x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -30 + 35x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 7x + -1x2) = 0 Factor a trinomial. 5((-6 + x)(1 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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 = {6, 1}
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