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Simplifying (19x + 16)(14 + x) = 0 Reorder the terms: (16 + 19x)(14 + x) = 0 Multiply (16 + 19x) * (14 + x) (16(14 + x) + 19x * (14 + x)) = 0 ((14 * 16 + x * 16) + 19x * (14 + x)) = 0 ((224 + 16x) + 19x * (14 + x)) = 0 (224 + 16x + (14 * 19x + x * 19x)) = 0 (224 + 16x + (266x + 19x2)) = 0 Combine like terms: 16x + 266x = 282x (224 + 282x + 19x2) = 0 Solving 224 + 282x + 19x2 = 0 Solving for variable 'x'. Factor a trinomial. (14 + x)(16 + 19x) = 0Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Subproblem 2
Set the factor '(16 + 19x)' equal to zero and attempt to solve: Simplifying 16 + 19x = 0 Solving 16 + 19x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 19x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 19x = 0 + -16 19x = 0 + -16 Combine like terms: 0 + -16 = -16 19x = -16 Divide each side by '19'. x = -0.8421052632 Simplifying x = -0.8421052632Solution
x = {-14, -0.8421052632}
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