Solve =0quad2.4t^2=sqrt{1.44t^4+x}

$$= 0 \quad 2.4 t ^ { 2 } = \sqrt { 1.44 t ^ { 4 } + x }$$

Solve for x

$$x=-\frac{36t^{4}}{25}$$

Steps for Solving Radical Equations

Multiply 0 and 2.4 to get 0.

$$0t^{2}=\sqrt{1.44t^{4}+x}$$

Anything times zero gives zero.

$$0=\sqrt{1.44t^{4}+x}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{1.44t^{4}+x}=0$$

Square both sides of the equation.

$$x+\frac{36t^{4}}{25}=0$$

Subtract 1.44t^{4} from both sides of the equation.

$$x+\frac{36t^{4}}{25}-\frac{36t^{4}}{25}=-\frac{36t^{4}}{25}$$

Subtracting 1.44t^{4} from itself leaves 0.

$$x=-\frac{36t^{4}}{25}$$

Solve for t (complex solution)

$$t=\left(\frac{1}{6}+\frac{1}{6}i\right)\sqrt{15}\sqrt[4]{x}$$

$$t=\left(-\frac{1}{6}-\frac{1}{6}i\right)\sqrt{15}\sqrt[4]{x}$$

$$t=\left(-\frac{1}{6}+\frac{1}{6}i\right)\sqrt{15}\sqrt[4]{x}$$

$$t=\left(\frac{1}{6}-\frac{1}{6}i\right)\sqrt{15}\sqrt[4]{x}$$

Solve for t

$$\left\{\begin{matrix}\\t=0\text{, }&\text{unconditionally}\\t=-\frac{\sqrt{30}\sqrt[4]{-x}}{6}\text{; }t=\frac{\sqrt{30}\sqrt[4]{-x}}{6}\text{, }&x\leq 0\end{matrix}\right.$$