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Simplifying 30x2 + 5x = 60 Reorder the terms: 5x + 30x2 = 60 Solving 5x + 30x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 5x + 30x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 5x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-12 + x + 6x2) = 0 Factor a trinomial. 5((-3 + -2x)(4 + -3x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-1.5, 1.333333333}
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