Solve (b)^2+(a-b)^2=2(a^2+b^2)

$$( b ) ^ { 2 } + ( a - b ) ^ { 2 } = 2 ( a ^ { 2 } + b ^ { 2 } )$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=-\frac{a}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$b^{2}+a^{2}-2ab+b^{2}=2\left(a^{2}+b^{2}\right)$$

Combine b^{2} and b^{2} to get 2b^{2}.

$$2b^{2}+a^{2}-2ab=2\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply 2 by a^{2}+b^{2}.

$$2b^{2}+a^{2}-2ab=2a^{2}+2b^{2}$$

Subtract 2b^{2} from both sides.

$$2b^{2}+a^{2}-2ab-2b^{2}=2a^{2}$$

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

$$a^{2}-2ab=2a^{2}$$

Subtract a^{2} from both sides.

$$-2ab=2a^{2}-a^{2}$$

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

$$-2ab=a^{2}$$

The equation is in standard form.

$$\left(-2a\right)b=a^{2}$$

Divide both sides by -2a.

$$\frac{\left(-2a\right)b}{-2a}=\frac{a^{2}}{-2a}$$

Dividing by -2a undoes the multiplication by -2a.

$$b=\frac{a^{2}}{-2a}$$

Divide a^{2} by -2a.

$$b=-\frac{a}{2}$$

Solve for b

$$\left\{\begin{matrix}\\b=-\frac{a}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$b^{2}+a^{2}-2ab+b^{2}=2\left(a^{2}+b^{2}\right)$$

Combine b^{2} and b^{2} to get 2b^{2}.

$$2b^{2}+a^{2}-2ab=2\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply 2 by a^{2}+b^{2}.

$$2b^{2}+a^{2}-2ab=2a^{2}+2b^{2}$$

Subtract 2b^{2} from both sides.

$$2b^{2}+a^{2}-2ab-2b^{2}=2a^{2}$$

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

$$a^{2}-2ab=2a^{2}$$

Subtract a^{2} from both sides.

$$-2ab=2a^{2}-a^{2}$$

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

$$-2ab=a^{2}$$

The equation is in standard form.

$$\left(-2a\right)b=a^{2}$$

Divide both sides by -2a.

$$\frac{\left(-2a\right)b}{-2a}=\frac{a^{2}}{-2a}$$

Dividing by -2a undoes the multiplication by -2a.

$$b=\frac{a^{2}}{-2a}$$

Divide a^{2} by -2a.

$$b=-\frac{a}{2}$$

Solve for a

$$a=-2b$$

$$a=0$$