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Simplifying (X + 14)(2X + 5) + (X + 14)(8X + 0) = 0 Reorder the terms: (14 + X)(2X + 5) + (X + 14)(8X + 0) = 0 Reorder the terms: (14 + X)(5 + 2X) + (X + 14)(8X + 0) = 0 Multiply (14 + X) * (5 + 2X) (14(5 + 2X) + X(5 + 2X)) + (X + 14)(8X + 0) = 0 ((5 * 14 + 2X * 14) + X(5 + 2X)) + (X + 14)(8X + 0) = 0 ((70 + 28X) + X(5 + 2X)) + (X + 14)(8X + 0) = 0 (70 + 28X + (5 * X + 2X * X)) + (X + 14)(8X + 0) = 0 (70 + 28X + (5X + 2X2)) + (X + 14)(8X + 0) = 0 Combine like terms: 28X + 5X = 33X (70 + 33X + 2X2) + (X + 14)(8X + 0) = 0 Reorder the terms: 70 + 33X + 2X2 + (14 + X)(8X + 0) = 0 Reorder the terms: 70 + 33X + 2X2 + (14 + X)(0 + 8X) = 0 Remove the zero: 70 + 33X + 2X2 + (14 + X)(8X) = 0 Remove parenthesis around (8X) 70 + 33X + 2X2 + (14 + X) * 8X = 0 Reorder the terms for easier multiplication: 70 + 33X + 2X2 + 8X(14 + X) = 0 70 + 33X + 2X2 + (14 * 8X + X * 8X) = 0 70 + 33X + 2X2 + (112X + 8X2) = 0 Reorder the terms: 70 + 33X + 112X + 2X2 + 8X2 = 0 Combine like terms: 33X + 112X = 145X 70 + 145X + 2X2 + 8X2 = 0 Combine like terms: 2X2 + 8X2 = 10X2 70 + 145X + 10X2 = 0 Solving 70 + 145X + 10X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '5'. 5(14 + 29X + 2X2) = 0 Factor a trinomial. 5((14 + X)(1 + 2X)) = 0 Ignore the factor 5.Subproblem 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 '(1 + 2X)' equal to zero and attempt to solve: Simplifying 1 + 2X = 0 Solving 1 + 2X = 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 + 2X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2X = 0 + -1 2X = 0 + -1 Combine like terms: 0 + -1 = -1 2X = -1 Divide each side by '2'. X = -0.5 Simplifying X = -0.5Solution
X = {-14, -0.5}
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