Solve 8-t=sqrt{5t^2+64-16t}

$$8 - t = \sqrt { 5 t ^ { 2 } + 64 - 16 t }$$

Solve for t

$$t=0$$

Solution Steps

Square both sides of the equation.

$$\left(8-t\right)^{2}=\left(\sqrt{5t^{2}+64-16t}\right)^{2}$$

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

$$64-16t+t^{2}=\left(\sqrt{5t^{2}+64-16t}\right)^{2}$$

Calculate \sqrt{5t^{2}+64-16t} to the power of 2 and get 5t^{2}+64-16t.

$$64-16t+t^{2}=5t^{2}+64-16t$$

Subtract 5t^{2} from both sides.

$$64-16t+t^{2}-5t^{2}=64-16t$$

Combine t^{2} and -5t^{2} to get -4t^{2}.

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

Add 16t to both sides.

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

Combine -16t and 16t to get 0.

$$64-4t^{2}=64$$

Subtract 64 from both sides.

$$-4t^{2}=64-64$$

Subtract 64 from 64 to get 0.

$$-4t^{2}=0$$

Divide both sides by -4. Zero divided by any non-zero number gives zero.

$$t^{2}=0$$

Take the square root of both sides of the equation.

$$t=0 t=0$$

The equation is now solved. Solutions are the same.

$$t=0$$

Substitute 0 for t in the equation 8-t=\sqrt{5t^{2}+64-16t}.

$$8-0=\sqrt{5\times 0^{2}+64-16\times 0}$$

Simplify. The value t=0 satisfies the equation.

$$8=8$$

Equation 8-t=\sqrt{5t^{2}-16t+64} has a unique solution.

$$t=0$$