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Simplifying 30 = -5x2 + 30x + 5 Reorder the terms: 30 = 5 + 30x + -5x2 Solving 30 = 5 + 30x + -5x2 Solving for variable 'x'. Combine like terms: 30 + -5 = 25 25 + -30x + 5x2 = 5 + 30x + -5x2 + -5 + -30x + 5x2 Reorder the terms: 25 + -30x + 5x2 = 5 + -5 + 30x + -30x + -5x2 + 5x2 Combine like terms: 5 + -5 = 0 25 + -30x + 5x2 = 0 + 30x + -30x + -5x2 + 5x2 25 + -30x + 5x2 = 30x + -30x + -5x2 + 5x2 Combine like terms: 30x + -30x = 0 25 + -30x + 5x2 = 0 + -5x2 + 5x2 25 + -30x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 25 + -30x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -6x + x2) = 0 Factor a trinomial. 5((1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {1, 5}
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