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

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bc}{b+c}\text{, }&b\neq -c\\a\in \mathrm{C}\text{, }&c=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Square a+b+c.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}=a^{2}+b^{2}+c^{2}$$

Subtract a^{2} from both sides.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}-a^{2}=b^{2}+c^{2}$$

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

$$2ab+2ac+b^{2}+2bc+c^{2}=b^{2}+c^{2}$$

Subtract b^{2} from both sides.

$$2ab+2ac+2bc+c^{2}=b^{2}+c^{2}-b^{2}$$

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

$$2ab+2ac+2bc+c^{2}=c^{2}$$

Subtract 2bc from both sides.

$$2ab+2ac+c^{2}=c^{2}-2bc$$

Subtract c^{2} from both sides.

$$2ab+2ac=c^{2}-2bc-c^{2}$$

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

$$2ab+2ac=-2bc$$

Combine all terms containing a.

$$\left(2b+2c\right)a=-2bc$$

Divide both sides by 2b+2c.

$$\frac{\left(2b+2c\right)a}{2b+2c}=-\frac{2bc}{2b+2c}$$

Dividing by 2b+2c undoes the multiplication by 2b+2c.

$$a=-\frac{2bc}{2b+2c}$$

Divide -2bc by 2b+2c.

$$a=-\frac{bc}{b+c}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ac}{a+c}\text{, }&a\neq -c\\b\in \mathrm{C}\text{, }&c=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Square a+b+c.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}=a^{2}+b^{2}+c^{2}$$

Subtract b^{2} from both sides.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}-b^{2}=a^{2}+c^{2}$$

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

$$a^{2}+2ab+2ac+2bc+c^{2}=a^{2}+c^{2}$$

Subtract a^{2} from both sides.

$$2ab+2ac+2bc+c^{2}=a^{2}+c^{2}-a^{2}$$

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

$$2ab+2ac+2bc+c^{2}=c^{2}$$

Subtract 2ac from both sides.

$$2ab+2bc+c^{2}=c^{2}-2ac$$

Subtract c^{2} from both sides.

$$2ab+2bc=c^{2}-2ac-c^{2}$$

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

$$2ab+2bc=-2ac$$

Combine all terms containing b.

$$\left(2a+2c\right)b=-2ac$$

Divide both sides by 2a+2c.

$$\frac{\left(2a+2c\right)b}{2a+2c}=-\frac{2ac}{2a+2c}$$

Dividing by 2a+2c undoes the multiplication by 2a+2c.

$$b=-\frac{2ac}{2a+2c}$$

Divide -2ac by 2a+2c.

$$b=-\frac{ac}{a+c}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bc}{b+c}\text{, }&b\neq -c\\a\in \mathrm{R}\text{, }&c=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Square a+b+c.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}=a^{2}+b^{2}+c^{2}$$

Subtract a^{2} from both sides.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}-a^{2}=b^{2}+c^{2}$$

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

$$2ab+2ac+b^{2}+2bc+c^{2}=b^{2}+c^{2}$$

Subtract b^{2} from both sides.

$$2ab+2ac+2bc+c^{2}=b^{2}+c^{2}-b^{2}$$

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

$$2ab+2ac+2bc+c^{2}=c^{2}$$

Subtract 2bc from both sides.

$$2ab+2ac+c^{2}=c^{2}-2bc$$

Subtract c^{2} from both sides.

$$2ab+2ac=c^{2}-2bc-c^{2}$$

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

$$2ab+2ac=-2bc$$

Combine all terms containing a.

$$\left(2b+2c\right)a=-2bc$$

Divide both sides by 2b+2c.

$$\frac{\left(2b+2c\right)a}{2b+2c}=-\frac{2bc}{2b+2c}$$

Dividing by 2b+2c undoes the multiplication by 2b+2c.

$$a=-\frac{2bc}{2b+2c}$$

Divide -2bc by 2b+2c.

$$a=-\frac{bc}{b+c}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ac}{a+c}\text{, }&a\neq -c\\b\in \mathrm{R}\text{, }&c=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Square a+b+c.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}=a^{2}+b^{2}+c^{2}$$

Subtract b^{2} from both sides.

$$a^{2}+2ab+2ac+b^{2}+2bc+c^{2}-b^{2}=a^{2}+c^{2}$$

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

$$a^{2}+2ab+2ac+2bc+c^{2}=a^{2}+c^{2}$$

Subtract a^{2} from both sides.

$$2ab+2ac+2bc+c^{2}=a^{2}+c^{2}-a^{2}$$

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

$$2ab+2ac+2bc+c^{2}=c^{2}$$

Subtract 2ac from both sides.

$$2ab+2bc+c^{2}=c^{2}-2ac$$

Subtract c^{2} from both sides.

$$2ab+2bc=c^{2}-2ac-c^{2}$$

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

$$2ab+2bc=-2ac$$

Combine all terms containing b.

$$\left(2a+2c\right)b=-2ac$$

Divide both sides by 2a+2c.

$$\frac{\left(2a+2c\right)b}{2a+2c}=-\frac{2ac}{2a+2c}$$

Dividing by 2a+2c undoes the multiplication by 2a+2c.

$$b=-\frac{2ac}{2a+2c}$$

Divide -2ac by 2a+2c.

$$b=-\frac{ac}{a+c}$$