Solve 4t-25sqrt{t}=0

$$4 t - 25 \sqrt { t } = 0$$

Solve for t

$$t=0$$

$$t = \frac{625}{16} = 39\frac{1}{16} = 39.0625$$

Solution Steps

Subtract 4t from both sides of the equation.

$$-25\sqrt{t}=-4t$$

Square both sides of the equation.

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

Expand \left(-25\sqrt{t}\right)^{2}.

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

Calculate -25 to the power of 2 and get 625.

$$625\left(\sqrt{t}\right)^{2}=\left(-4t\right)^{2}$$

Calculate \sqrt{t} to the power of 2 and get t.

$$625t=\left(-4t\right)^{2}$$

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

$$625t=\left(-4\right)^{2}t^{2}$$

Calculate -4 to the power of 2 and get 16.

$$625t=16t^{2}$$

Subtract 16t^{2} from both sides.

$$625t-16t^{2}=0$$

Factor out t.

$$t\left(625-16t\right)=0$$

To find equation solutions, solve t=0 and 625-16t=0.

$$t=0 t=\frac{625}{16}$$

Substitute 0 for t in the equation 4t-25\sqrt{t}=0.

$$4\times 0-25\sqrt{0}=0$$

Simplify. The value t=0 satisfies the equation.

$$0=0$$

Substitute \frac{625}{16} for t in the equation 4t-25\sqrt{t}=0.

$$4\times \frac{625}{16}-25\sqrt{\frac{625}{16}}=0$$

Simplify. The value t=\frac{625}{16} satisfies the equation.

$$0=0$$

List all solutions of -25\sqrt{t}=-4t.

$$t=0 t=\frac{625}{16}$$