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Simplifying (X + 4)(X + 7) = 70 Reorder the terms: (4 + X)(X + 7) = 70 Reorder the terms: (4 + X)(7 + X) = 70 Multiply (4 + X) * (7 + X) (4(7 + X) + X(7 + X)) = 70 ((7 * 4 + X * 4) + X(7 + X)) = 70 ((28 + 4X) + X(7 + X)) = 70 (28 + 4X + (7 * X + X * X)) = 70 (28 + 4X + (7X + X2)) = 70 Combine like terms: 4X + 7X = 11X (28 + 11X + X2) = 70 Solving 28 + 11X + X2 = 70 Solving for variable 'X'. Reorder the terms: 28 + -70 + 11X + X2 = 70 + -70 Combine like terms: 28 + -70 = -42 -42 + 11X + X2 = 70 + -70 Combine like terms: 70 + -70 = 0 -42 + 11X + X2 = 0 Factor a trinomial. (-14 + -1X)(3 + -1X) = 0Subproblem 1
Set the factor '(-14 + -1X)' equal to zero and attempt to solve: Simplifying -14 + -1X = 0 Solving -14 + -1X = 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 + -1X = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1X = 0 + 14 -1X = 0 + 14 Combine like terms: 0 + 14 = 14 -1X = 14 Divide each side by '-1'. X = -14 Simplifying X = -14Subproblem 2
Set the factor '(3 + -1X)' equal to zero and attempt to solve: Simplifying 3 + -1X = 0 Solving 3 + -1X = 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 + -1X = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1X = 0 + -3 -1X = 0 + -3 Combine like terms: 0 + -3 = -3 -1X = -3 Divide each side by '-1'. X = 3 Simplifying X = 3Solution
X = {-14, 3}
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