Answer:
x = 5 or x = 6
Step-by-step 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}.
