Solve (8-4t)^2+6^2=(4t)^2

$$( 8 - 4 t ) ^ { 2 } + 6 ^ { 2 } = ( 4 t ) ^ { 2 }$$

Solve for t

$$t = \frac{25}{16} = 1\frac{9}{16} = 1.5625$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-4t\right)^{2}.

$$64-64t+16t^{2}+6^{2}=\left(4t\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$64-64t+16t^{2}+36=\left(4t\right)^{2}$$

Add 64 and 36 to get 100.

$$100-64t+16t^{2}=\left(4t\right)^{2}$$

Expand \left(4t\right)^{2}.

$$100-64t+16t^{2}=4^{2}t^{2}$$

Calculate 4 to the power of 2 and get 16.

$$100-64t+16t^{2}=16t^{2}$$

Subtract 16t^{2} from both sides.

$$100-64t+16t^{2}-16t^{2}=0$$

Combine 16t^{2} and -16t^{2} to get 0.

$$100-64t=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-64t=-100$$

Divide both sides by -64.

$$t=\frac{-100}{-64}$$

Reduce the fraction \frac{-100}{-64} to lowest terms by extracting and canceling out -4.

$$t=\frac{25}{16}$$