Question

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

x^2 - 8x + 30 = 3x

Answer 1

x = 5 or x = 6

Explanation:

Given equation is :

x²-8x+30 = 3x

adding -3x to both sides of above equation, we get

x²-8x+30-3x = 3x-3x

add like terms

x²-11x+30 = 0

we solve this equation by factoring.

split the middle term so that the product of two numbers should be 30 and the sum is -11.

x²-6x-5x+30 = 0

make two groups

x(x-6)-5(x-6) = 0

take (x-6) as common

(x-6)(x-5) = 0

Applying Zero-Product Property to above equation,we get

x-6 = 0 or x-5 = 0

first solve x-6 = 0

adding 6 to both sides of above equation,we get

x-6+6 = 0+6

x+0 = 6

x = 6

secondly, solve this x-5 = 0

adding 5 to above equation , we get

x-5+5 = 0+5

x +0 = 5

x = 5

Hence, the solution of x²-8x+30 = 3x is {6,5}.

Answer 2

x=5 x=6

Explanation:

x^2 - 8x + 30 = 3x

Subtract 3x from each side

x^2 - 8x-3x + 30 = 3x-3x

x^2 - 11x + 30 = 0

What 2 numbers multiply to 30 and add to -11

-5*-6 = 30

-5+-6 = -11

(x-5) (x-6) =0

Using the zero product property

x-5 = 0 and x-6 =0

x-5+5 =0+5 and x-6+6 =0+6

x=5 x=6