Solve 3^2+(4-2t)^2=(2t)^2

$$3 ^ { 2 } + ( 4 - 2 t ) ^ { 2 } = ( 2 t ) ^ { 2 }$$

Solve for t

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

Steps for Solving Linear Equation

Calculate 3 to the power of 2 and get 9.

$$9+\left(4-2t\right)^{2}=\left(2t\right)^{2}$$

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

$$9+16-16t+4t^{2}=\left(2t\right)^{2}$$

Add 9 and 16 to get 25.

$$25-16t+4t^{2}=\left(2t\right)^{2}$$

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

$$25-16t+4t^{2}=2^{2}t^{2}$$

Calculate 2 to the power of 2 and get 4.

$$25-16t+4t^{2}=4t^{2}$$

Subtract 4t^{2} from both sides.

$$25-16t+4t^{2}-4t^{2}=0$$

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

$$25-16t=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-16t=-25$$

Divide both sides by -16.

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

Fraction \frac{-25}{-16} can be simplified to \frac{25}{16} by removing the negative sign from both the numerator and the denominator.

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