OG详解-OG2 数学1 Q7

The correct answer is 5. Multiplying both sides of the given equation by x + 6 results in 55 = x (x +6). Applying the distributive property of multiplication to the right-hand side of this equation results in 55 = x² + 6x. Subtracting 55 from both sides of this equation results in 0 = x²+6x-55. The right-hand side of this equation can be rewritten by factoring. The two values that multiply to -55 and add to 6 are 11 and -5. It follows that the equation 0=x²+6x-55 can be rewritten as 0 = (x+11) (x-5). Setting each factor equal to 0 yields two equations: x +11= 0 and x - 5 = 0. Subtracting 11 from both sides of the equation x +11=0 results in x =-11. Adding 5 to both sides of the equation x - 5 = 0 results in x =5. Therefore, the positive solution to the given equation is 5.