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Simplifying -18x2 = 48x + 14 Reorder the terms: -18x2 = 14 + 48x Solving -18x2 = 14 + 48x Solving for variable 'x'. Reorder the terms: -14 + -48x + -18x2 = 14 + 48x + -14 + -48x Reorder the terms: -14 + -48x + -18x2 = 14 + -14 + 48x + -48x Combine like terms: 14 + -14 = 0 -14 + -48x + -18x2 = 0 + 48x + -48x -14 + -48x + -18x2 = 48x + -48x Combine like terms: 48x + -48x = 0 -14 + -48x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(7 + 24x + 9x2) = 0 Factor a trinomial. -2((7 + 3x)(1 + 3x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-2.333333333, -0.3333333333}
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