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Simplifying -120x2 + 70x = 5 Reorder the terms: 70x + -120x2 = 5 Solving 70x + -120x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 70x + -120x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 70x + -120x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + 14x + -24x2) = 0 Factor a trinomial. 5((-1 + 2x)(1 + -12x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(1 + -12x)' equal to zero and attempt to solve: Simplifying 1 + -12x = 0 Solving 1 + -12x = 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 + -12x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12x = 0 + -1 -12x = 0 + -1 Combine like terms: 0 + -1 = -1 -12x = -1 Divide each side by '-12'. x = 0.08333333333 Simplifying x = 0.08333333333Solution
x = {0.5, 0.08333333333}
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