Find two numbers whose sum is 19 if the sum of their squares is 185

the first number:8
the second number: 11
x+y=19
-y -y

x=19-y substitute the values in
x^2+y^2=185
(19-y)^2+y^2=185
361-38y+y^2+y^2=185
361-38y+2y^2=185
-185 -185

361-38y+2y^2-185=0 combine like terms
176-38y+2y^2=0 commutative property
2y^2-38y+176=0 divide both sides by 2

2
y^2-19y+88=0 solve the quadratic equation
y= -(19)+square root of (-19)^2-4(1)(88)
simplify
2(1)
y= (19)+ square root of 361-4(88)

2
y=19+square root of 361-352

2
Y=19 square root of 9

2
Y=19+3
-

2
y=19-3 16
= 8
2 2
y=19+3 22
=11
2 2