The sum of the squares of two consecutive even integers is 452. Find the integers.

Question

I know the two numbers are 14 and 16, but I don't understand how to make a quadratic equation in order to show my steps. 

Answer 1

x and x+2 are the integers

x²+(x+2)²=452

x²+x²+4x+4=452

2x²+4x+4-452=0

2x²+4x-448=0

divide both sides by 2

x²+2x-224=0

224=2*2*2*2*2*7=(2*2*2*2)*(2*7)=16*14 and 16-14=2

factor

(x+16)(x-14)=0

x-14=0

x=14

x+2=16