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Simplifying 6(x2 + 4x + 4) + 9(x + 2) = 0 Reorder the terms: 6(4 + 4x + x2) + 9(x + 2) = 0 (4 * 6 + 4x * 6 + x2 * 6) + 9(x + 2) = 0 (24 + 24x + 6x2) + 9(x + 2) = 0 Reorder the terms: 24 + 24x + 6x2 + 9(2 + x) = 0 24 + 24x + 6x2 + (2 * 9 + x * 9) = 0 24 + 24x + 6x2 + (18 + 9x) = 0 Reorder the terms: 24 + 18 + 24x + 9x + 6x2 = 0 Combine like terms: 24 + 18 = 42 42 + 24x + 9x + 6x2 = 0 Combine like terms: 24x + 9x = 33x 42 + 33x + 6x2 = 0 Solving 42 + 33x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 11x + 2x2) = 0 Factor a trinomial. 3((7 + 2x)(2 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-3.5, -2}
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