Solve x^2-4x+49+y^2=x^2-2x+1+y^2+12y+36

$$x ^ { 2 } - 4 x + 49 + y ^ { 2 } = x ^ { 2 } - 2 x + 1 + y ^ { 2 } + 12 y + 36$$

Solve for x

$$x=6-6y$$

Steps for Solving Linear Equation

Add 1 and 36 to get 37.

$$x^{2}-4x+49+y^{2}=x^{2}-2x+37+y^{2}+12y$$

Subtract x^{2} from both sides.

$$x^{2}-4x+49+y^{2}-x^{2}=-2x+37+y^{2}+12y$$

Combine x^{2} and -x^{2} to get 0.

$$-4x+49+y^{2}=-2x+37+y^{2}+12y$$

Add 2x to both sides.

$$-4x+49+y^{2}+2x=37+y^{2}+12y$$

Combine -4x and 2x to get -2x.

$$-2x+49+y^{2}=37+y^{2}+12y$$

Subtract 49 from both sides.

$$-2x+y^{2}=37+y^{2}+12y-49$$

Subtract 49 from 37 to get -12.

$$-2x+y^{2}=-12+y^{2}+12y$$

Subtract y^{2} from both sides.

$$-2x=-12+y^{2}+12y-y^{2}$$

Combine y^{2} and -y^{2} to get 0.

$$-2x=-12+12y$$

The equation is in standard form.

$$-2x=12y-12$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{12y-12}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{12y-12}{-2}$$

Divide -12+12y by -2.

$$x=6-6y$$

Solve for y

$$y=-\frac{x}{6}+1$$

Steps for Solving Linear Equation

Add 1 and 36 to get 37.

$$x^{2}-4x+49+y^{2}=x^{2}-2x+37+y^{2}+12y$$

Subtract y^{2} from both sides.

$$x^{2}-4x+49+y^{2}-y^{2}=x^{2}-2x+37+12y$$

Combine y^{2} and -y^{2} to get 0.

$$x^{2}-4x+49=x^{2}-2x+37+12y$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-2x+37+12y=x^{2}-4x+49$$

Subtract x^{2} from both sides.

$$-2x+37+12y=x^{2}-4x+49-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-2x+37+12y=-4x+49$$

Add 2x to both sides.

$$37+12y=-4x+49+2x$$

Combine -4x and 2x to get -2x.

$$37+12y=-2x+49$$

Subtract 37 from both sides.

$$12y=-2x+49-37$$

Subtract 37 from 49 to get 12.

$$12y=-2x+12$$

The equation is in standard form.

$$12y=12-2x$$

Divide both sides by 12.

$$\frac{12y}{12}=\frac{12-2x}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$y=\frac{12-2x}{12}$$

Divide -2x+12 by 12.

$$y=-\frac{x}{6}+1$$