Solve (8-2t)^2+64=(14-2t)^2

$$( 8 - 2 t ) ^ { 2 } + 64 = ( 14 - 2 t ) ^ { 2 }$$

Solve for t

$$t = \frac{17}{6} = 2\frac{5}{6} \approx 2.833333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-2t\right)^{2}.

$$64-32t+4t^{2}+64=\left(14-2t\right)^{2}$$

Add 64 and 64 to get 128.

$$128-32t+4t^{2}=\left(14-2t\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(14-2t\right)^{2}.

$$128-32t+4t^{2}=196-56t+4t^{2}$$

Add 56t to both sides.

$$128-32t+4t^{2}+56t=196+4t^{2}$$

Combine -32t and 56t to get 24t.

$$128+24t+4t^{2}=196+4t^{2}$$

Subtract 4t^{2} from both sides.

$$128+24t+4t^{2}-4t^{2}=196$$

Combine 4t^{2} and -4t^{2} to get 0.

$$128+24t=196$$

Subtract 128 from both sides.

$$24t=196-128$$

Subtract 128 from 196 to get 68.

$$24t=68$$

Divide both sides by 24.

$$t=\frac{68}{24}$$

Reduce the fraction \frac{68}{24} to lowest terms by extracting and canceling out 4.

$$t=\frac{17}{6}$$