Answer:
x=−y
Explanation:
x
2
+y
2
+2xy=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x
2
+2yx+y
2
=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 1 for a, 2y for b, and y
2
for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2
−2y±
(2y)
2
−4y
2
Square 2y.
x=
2
−2y±
4y
2
−4y
2
Add 4y
2
to −4y
2
.
x=
2
−2y±
0
Take the square root of 0.
x=−
2
2y
Divide −2y by 2.
x=−y