Solve (sqrt{5-2t+t^{2}})^2+(2sqrt{13})^2=(sqrt{25+6t+t^2})^2

$$( \sqrt { 5 - 2 t + t ^ { 2 } } ) ^ { 2 } + ( 2 \sqrt { 13 } ) ^ { 2 } = ( \sqrt { 25 + 6 t + t ^ { 2 } } ) ^ { 2 }$$

Solve for t

$$t=4$$

Steps for Solving Linear Equation

Calculate \sqrt{5-2t+t^{2}} to the power of 2 and get 5-2t+t^{2}.

$$5-2t+t^{2}+\left(2\sqrt{13}\right)^{2}=\left(\sqrt{25+6t+t^{2}}\right)^{2}$$

Expand \left(2\sqrt{13}\right)^{2}.

$$5-2t+t^{2}+2^{2}\left(\sqrt{13}\right)^{2}=\left(\sqrt{25+6t+t^{2}}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$5-2t+t^{2}+4\left(\sqrt{13}\right)^{2}=\left(\sqrt{25+6t+t^{2}}\right)^{2}$$

The square of \sqrt{13} is 13.

$$5-2t+t^{2}+4\times 13=\left(\sqrt{25+6t+t^{2}}\right)^{2}$$

Multiply 4 and 13 to get 52.

$$5-2t+t^{2}+52=\left(\sqrt{25+6t+t^{2}}\right)^{2}$$

Add 5 and 52 to get 57.

$$57-2t+t^{2}=\left(\sqrt{25+6t+t^{2}}\right)^{2}$$

Calculate \sqrt{25+6t+t^{2}} to the power of 2 and get 25+6t+t^{2}.

$$57-2t+t^{2}=25+6t+t^{2}$$

Subtract 6t from both sides.

$$57-2t+t^{2}-6t=25+t^{2}$$

Combine -2t and -6t to get -8t.

$$57-8t+t^{2}=25+t^{2}$$

Subtract t^{2} from both sides.

$$57-8t+t^{2}-t^{2}=25$$

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

$$57-8t=25$$

Subtract 57 from both sides.

$$-8t=25-57$$

Subtract 57 from 25 to get -32.

$$-8t=-32$$

Divide both sides by -8.

$$t=\frac{-32}{-8}$$

Divide -32 by -8 to get 4.

$$t=4$$