Solve each quadratic equation by factoring and using the zero product property.

14x - 49 = x^2

x=7 multiplicity of 2

Step-by-step explanation:

14x - 49 = x^2

Subtract x^2 from each side

-x^2 + 14x - 49 = x^2-x^2

-x^2 + 14x - 49 = 0

Multiply by - 1

x^2 - 14x + 49 = 0

What 2 numbers multiply together to give you 49 and add together to give you - 14

7*-7 = 49

-7+-7 = - 14

(x-7) (x-7) = 0

Using the zero product property

x-7 = 0 x-7 = 0

x-7+7 = 0+7 x-7+7 = 0+7

x = 7 x=7

x = 7

Step-by-step explanation:

Given equation is:

14x-49 = x²

adding - x² to both sides of equation, we get

-x²+14x-49 = - x²+x²

-x²+14x+49 = 0

take - 1 as common

-1 (x²-14x-49) = 0

now multiplying above equation to - 1, we get

x²-14x-49 = 0

Now, above equation is in general equation.

split the middle term of above equation so that the product of two terms should be 49 and sum be - 14.

x²-7x-7x-49 = 0

make two groups

x (x-7) - 7 (x-7) = 0

take (x-7) as common

(x-7) (x-7) = 0

Now applying Zero-Product Property to above equation, we get

x-7 = 0 or x-7 = 0

as both are same, hence

x-7 = 0

adding 7 to both sides of above equation, we get

x-7+7 = 0+7

x+0 = 7

x = 7 which is the answer.