Question

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

14x - 49 = x^2

Answer 1

x = 7

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.

Answer 2

x=7 multiplicity of 2

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