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Simplifying 5x2 = -30 + 35x Solving 5x2 = -30 + 35x Solving for variable 'x'. Reorder the terms: 30 + -35x + 5x2 = -30 + 35x + 30 + -35x Reorder the terms: 30 + -35x + 5x2 = -30 + 30 + 35x + -35x Combine like terms: -30 + 30 = 0 30 + -35x + 5x2 = 0 + 35x + -35x 30 + -35x + 5x2 = 35x + -35x Combine like terms: 35x + -35x = 0 30 + -35x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -7x + x2) = 0 Factor a trinomial. 5((1 + -1x)(6 + -1x)) = 0 Ignore the factor 5.Subproblem 1
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 = 1Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {1, 6}
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