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Simplifying (X + -5)(X + -7) + -9 = (X + -6)(X + 6) Reorder the terms: (-5 + X)(X + -7) + -9 = (X + -6)(X + 6) Reorder the terms: (-5 + X)(-7 + X) + -9 = (X + -6)(X + 6) Multiply (-5 + X) * (-7 + X) (-5(-7 + X) + X(-7 + X)) + -9 = (X + -6)(X + 6) ((-7 * -5 + X * -5) + X(-7 + X)) + -9 = (X + -6)(X + 6) ((35 + -5X) + X(-7 + X)) + -9 = (X + -6)(X + 6) (35 + -5X + (-7 * X + X * X)) + -9 = (X + -6)(X + 6) (35 + -5X + (-7X + X2)) + -9 = (X + -6)(X + 6) Combine like terms: -5X + -7X = -12X (35 + -12X + X2) + -9 = (X + -6)(X + 6) Reorder the terms: 35 + -9 + -12X + X2 = (X + -6)(X + 6) Combine like terms: 35 + -9 = 26 26 + -12X + X2 = (X + -6)(X + 6) Reorder the terms: 26 + -12X + X2 = (-6 + X)(X + 6) Reorder the terms: 26 + -12X + X2 = (-6 + X)(6 + X) Multiply (-6 + X) * (6 + X) 26 + -12X + X2 = (-6(6 + X) + X(6 + X)) 26 + -12X + X2 = ((6 * -6 + X * -6) + X(6 + X)) 26 + -12X + X2 = ((-36 + -6X) + X(6 + X)) 26 + -12X + X2 = (-36 + -6X + (6 * X + X * X)) 26 + -12X + X2 = (-36 + -6X + (6X + X2)) Combine like terms: -6X + 6X = 0 26 + -12X + X2 = (-36 + 0 + X2) 26 + -12X + X2 = (-36 + X2) Add '-1X2' to each side of the equation. 26 + -12X + X2 + -1X2 = -36 + X2 + -1X2 Combine like terms: X2 + -1X2 = 0 26 + -12X + 0 = -36 + X2 + -1X2 26 + -12X = -36 + X2 + -1X2 Combine like terms: X2 + -1X2 = 0 26 + -12X = -36 + 0 26 + -12X = -36 Solving 26 + -12X = -36 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + -12X = -36 + -26 Combine like terms: 26 + -26 = 0 0 + -12X = -36 + -26 -12X = -36 + -26 Combine like terms: -36 + -26 = -62 -12X = -62 Divide each side by '-12'. X = 5.166666667 Simplifying X = 5.166666667
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