Question

Solve x^2=14x-49 using any method

Answer 1

Answer:

x=7

Step-by-step explanation:

x^2=14x-49

x^2-14x+49=0

(x-7)^2=0

x-7=0

x=7

Answer 2

Answer:

x = 7

Step-by-step explanation:

First, you can start by subtracting 14x - 49 from both sides to get 0 on the left side:

x^2=14x-49

-(14x - 49) -(14x - 49)

x^2 - 14x + 49 = 0

Now, we can realize that this equation resembles a perfect square trinomial, which would be in the form a^2 - 2ab + b^2. This factors to (a - b)^2. We can say that x^2 corresponds to a^2 and 49 corresponds to b^2. We can wrote two equations to solve for a and b:

a^2 = x^2

a = x

b^2 = 49

b = 7

This means we can factor x^2 - 14x + 49 into (x - 7)^2.

Now we can use the zero product property:

(x - 7)^2 = 0

x - 7 = 0

x = 7