A word problem on algebra linear equations

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Let's see a word problem from 8th grade word problems worksheets.

Question:-

Jack is thinking two positive numbers.one of them is 4 more than the other and the sum of their squares is 208.what are the two numbers?

Answer:-

Let one number be x.

the other number is 4 more ,x+4

given sum of the squares =208

x²+(x+4)²=208

x²+x²+8x+16=208

expanding the 2nd term

2x²+8x+16=208

dividing by 2 as it is common for all terms

x²+4x+8=104

subtract 104 on both sides

x²+4x-96=0

x²+12x-8x-96=0

x(x+12)-8(x+12)=0

(x+12)(x-8)=0

x=-12 or x=8

here we want only positive number ,so x=8

and the numbers are 8 and 12