Find the x and y Intercepts x^2+y^2+6x-6y-46=0

Problem

x^2+y^2+6*x−6*y−46=0

Solution

1. Find the x-intercepts by setting y=0 in the original equation.

x^2+(0)^2+6*x−6*(0)−46=0

x^2+6*x−46=0

2. Apply the quadratic formula to solve for x where a=1 b=6 and c=−46

x=(−6±√(,6^2−4*(1)*(−46)))/(2*(1))

x=(−6±√(,36+184))/2

x=(−6±√(,220))/2

3. Simplify the radical and solve for x

x=(−6±2√(,55))/2

x=−3±√(,55)

4. Find the y-intercepts by setting x=0 in the original equation.

(0)^2+y^2+6*(0)−6*y−46=0

y^2−6*y−46=0

5. Apply the quadratic formula to solve for y where a=1 b=−6 and c=−46

y=(−(−6)±√(,(−6)^2−4*(1)*(−46)))/(2*(1))

y=(6±√(,36+184))/2

y=(6±√(,220))/2

6. Simplify the radical and solve for y

y=(6±2√(,55))/2

y=3±√(,55)

Final Answer

x-intercepts: *(−3±√(,55),0), y-intercepts: *(0,3±√(,55))

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