Find the Vertex Form x^2+y^2+16x-18y+145=25

Problem

x2+y2+16*x−18*y+145=25

Solution

1. Group the terms by variable and move the constant term to the right side of the equation.

x2+16*x+y2−18*y=25−145

x2+16*x+y2−18*y=−120

2. Complete the square for the x terms by adding (16/2)2=64 to both sides.

x2+16*x+64+y2−18*y=−120+64

3. Complete the square for the y terms by adding ((−18)/2)2=81 to both sides.

x2+16*x+64+y2−18*y+81=−120+64+81

4. Factor the quadratic trinomials into perfect square binomials and simplify the right side.

(x+8)2+(y−9)2=25

Final Answer

x2+y2+16*x−18*y+145=25⇒(x+8)2+(y−9)2=25

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