Solve 0.785=1/2x-10xt^2

$$0.785 = 1 / 2 x - 10 x t ^ { 2 }$$

Solve for x (complex solution)

$$x=-\frac{157}{100\left(20t^{2}-1\right)}$$

$$t\neq -\frac{\sqrt{5}}{10}\text{ and }t\neq \frac{\sqrt{5}}{10}$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}x-10xt^{2}=0.785$$

Combine all terms containing x.

$$\left(\frac{1}{2}-10t^{2}\right)x=0.785$$

Divide both sides by \frac{1}{2}-10t^{2}.

$$\frac{\left(\frac{1}{2}-10t^{2}\right)x}{\frac{1}{2}-10t^{2}}=\frac{0.785}{\frac{1}{2}-10t^{2}}$$

Dividing by \frac{1}{2}-10t^{2} undoes the multiplication by \frac{1}{2}-10t^{2}.

$$x=\frac{0.785}{\frac{1}{2}-10t^{2}}$$

Divide 0.785 by \frac{1}{2}-10t^{2}.

$$x=\frac{157}{100\left(1-20t^{2}\right)}$$

Solve for x

$$x=-\frac{157}{100\left(20t^{2}-1\right)}$$

$$|t|\neq \frac{\sqrt{5}}{10}$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}x-10xt^{2}=0.785$$

Combine all terms containing x.

$$\left(\frac{1}{2}-10t^{2}\right)x=0.785$$

Divide both sides by \frac{1}{2}-10t^{2}.

$$\frac{\left(\frac{1}{2}-10t^{2}\right)x}{\frac{1}{2}-10t^{2}}=\frac{0.785}{\frac{1}{2}-10t^{2}}$$

Dividing by \frac{1}{2}-10t^{2} undoes the multiplication by \frac{1}{2}-10t^{2}.

$$x=\frac{0.785}{\frac{1}{2}-10t^{2}}$$

Divide 0.785 by \frac{1}{2}-10t^{2}.

$$x=\frac{157}{100\left(1-20t^{2}\right)}$$

Solve for t (complex solution)

$$t=-\frac{\sqrt{500-\frac{785}{x}}}{100}$$

$$t=\frac{\sqrt{500-\frac{785}{x}}}{100}\text{, }x\neq 0$$

Solve for t

$$t=\frac{\sqrt{500-\frac{785}{x}}}{100}$$

$$t=-\frac{\sqrt{500-\frac{785}{x}}}{100}\text{, }x\geq \frac{157}{100}\text{ or }x<0$$