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Simplifying 19x2 + 100x + 166 = 6 + 4x2 Reorder the terms: 166 + 100x + 19x2 = 6 + 4x2 Solving 166 + 100x + 19x2 = 6 + 4x2 Solving for variable 'x'. Reorder the terms: 166 + -6 + 100x + 19x2 + -4x2 = 6 + 4x2 + -6 + -4x2 Combine like terms: 166 + -6 = 160 160 + 100x + 19x2 + -4x2 = 6 + 4x2 + -6 + -4x2 Combine like terms: 19x2 + -4x2 = 15x2 160 + 100x + 15x2 = 6 + 4x2 + -6 + -4x2 Reorder the terms: 160 + 100x + 15x2 = 6 + -6 + 4x2 + -4x2 Combine like terms: 6 + -6 = 0 160 + 100x + 15x2 = 0 + 4x2 + -4x2 160 + 100x + 15x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 160 + 100x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(32 + 20x + 3x2) = 0 Factor a trinomial. 5((4 + x)(8 + 3x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Divide each side by '3'. x = -2.666666667 Simplifying x = -2.666666667Solution
x = {-4, -2.666666667}
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