55 x + 6 = x What is the positive solution to the given equation?

Question

Accepted Answer

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 multipliion to the right-hand side of this equation results in 55 = x 2 + 6 x . Subtracting 55 from both sides of this equation results in 0 = x 2 + 6 x - 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 = x 2 + 6 x - 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 .

Question 55-x-6