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Simplifying 12x2 + 48x + 23 = -22 Reorder the terms: 23 + 48x + 12x2 = -22 Solving 23 + 48x + 12x2 = -22 Solving for variable 'x'. Reorder the terms: 23 + 22 + 48x + 12x2 = -22 + 22 Combine like terms: 23 + 22 = 45 45 + 48x + 12x2 = -22 + 22 Combine like terms: -22 + 22 = 0 45 + 48x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 16x + 4x2) = 0 Factor a trinomial. 3((5 + 2x)(3 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 2
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 = -1.5Solution
x = {-2.5, -1.5}
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