Solve (x+y+a)^2-a^2-2ax-x^2=?.23

$$( x + y + a ) ^ { 2 } - a ^ { 2 } - 2 a x - x ^ { 2 } = ? .23$$

Solve for a

$$a=-\frac{y}{2}-x+\frac{23}{200y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Square x+y+a.

$$x^{2}+2ax+2xy+y^{2}+2ay+a^{2}-a^{2}-2ax-x^{2}=0.23$$

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

$$x^{2}+2ax+2xy+y^{2}+2ay-2ax-x^{2}=0.23$$

Combine 2ax and -2ax to get 0.

$$x^{2}+2xy+y^{2}+2ay-x^{2}=0.23$$

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

$$2xy+y^{2}+2ay=0.23$$

Subtract 2xy from both sides.

$$y^{2}+2ay=0.23-2xy$$

Subtract y^{2} from both sides.

$$2ay=0.23-2xy-y^{2}$$

The equation is in standard form.

$$2ya=0.23-y^{2}-2xy$$

Divide both sides by 2y.

$$\frac{2ya}{2y}=\frac{0.23-y^{2}-2xy}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$a=\frac{0.23-y^{2}-2xy}{2y}$$

Divide 0.23-2xy-y^{2} by 2y.

$$a=-\frac{y}{2}-x+\frac{23}{200y}$$

Solve for x

$$x=-\frac{y}{2}-a+\frac{23}{200y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Square x+y+a.

$$x^{2}+2ax+2xy+y^{2}+2ay+a^{2}-a^{2}-2ax-x^{2}=0.23$$

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

$$x^{2}+2ax+2xy+y^{2}+2ay-2ax-x^{2}=0.23$$

Combine 2ax and -2ax to get 0.

$$x^{2}+2xy+y^{2}+2ay-x^{2}=0.23$$

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

$$2xy+y^{2}+2ay=0.23$$

Subtract y^{2} from both sides.

$$2xy+2ay=0.23-y^{2}$$

Subtract 2ay from both sides.

$$2xy=0.23-y^{2}-2ay$$

The equation is in standard form.

$$2yx=0.23-2ay-y^{2}$$

Divide both sides by 2y.

$$\frac{2yx}{2y}=\frac{0.23-2ay-y^{2}}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$x=\frac{0.23-2ay-y^{2}}{2y}$$

Divide 0.23-y^{2}-2ay by 2y.

$$x=-\frac{y}{2}-a+\frac{23}{200y}$$