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

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

Solve for t

$$t = \frac{25}{18} = 1\frac{7}{18} \approx 1.388888889$$

Steps for Solving Linear Equation

Expand \left(3t\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$9t^{2}=\left(3-3t\right)^{2}+4^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3-3t\right)^{2}.

$$9t^{2}=9-18t+9t^{2}+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$9t^{2}=9-18t+9t^{2}+16$$

Add 9 and 16 to get 25.

$$9t^{2}=25-18t+9t^{2}$$

Add 18t to both sides.

$$9t^{2}+18t=25+9t^{2}$$

Subtract 9t^{2} from both sides.

$$9t^{2}+18t-9t^{2}=25$$

Combine 9t^{2} and -9t^{2} to get 0.

$$18t=25$$

Divide both sides by 18.

$$t=\frac{25}{18}$$