Solve 836/18+θ*x=3sqrt{x^2}

$$8 \frac{ 36 }{ 18 } + \theta \times x=3 \sqrt{ { x }^{ 2 } }$$

Solve for θ (complex solution)

$$\theta =-\frac{-3\sqrt{x^{2}}+10}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18.

$$8\times 18+36+18\theta x=54\sqrt{x^{2}}$$

Multiply 8 and 18 to get 144.

$$144+36+18\theta x=54\sqrt{x^{2}}$$

Add 144 and 36 to get 180.

$$180+18\theta x=54\sqrt{x^{2}}$$

Subtract 180 from both sides.

$$18\theta x=54\sqrt{x^{2}}-180$$

The equation is in standard form.

$$18x\theta =54\sqrt{x^{2}}-180$$

Divide both sides by 18x.

$$\frac{18x\theta }{18x}=\frac{54\sqrt{x^{2}}-180}{18x}$$

Dividing by 18x undoes the multiplication by 18x.

$$\theta =\frac{54\sqrt{x^{2}}-180}{18x}$$

Divide 54\sqrt{x^{2}}-180 by 18x.

$$\theta =\frac{3\sqrt{x^{2}}-10}{x}$$

Solve for θ

$$\theta =-\frac{-3|x|+10}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18.

$$8\times 18+36+18\theta x=54\sqrt{x^{2}}$$

Multiply 8 and 18 to get 144.

$$144+36+18\theta x=54\sqrt{x^{2}}$$

Add 144 and 36 to get 180.

$$180+18\theta x=54\sqrt{x^{2}}$$

Subtract 180 from both sides.

$$18\theta x=54\sqrt{x^{2}}-180$$

The equation is in standard form.

$$18x\theta =54\sqrt{x^{2}}-180$$

Divide both sides by 18x.

$$\frac{18x\theta }{18x}=\frac{54|x|-180}{18x}$$

Dividing by 18x undoes the multiplication by 18x.

$$\theta =\frac{54|x|-180}{18x}$$

Divide 54|x|-180 by 18x.

$$\theta =\frac{3|x|-10}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{10}{3-\theta }\text{, }&\theta \neq 3\text{ and }arg(\frac{x\theta +10}{3})<\pi \\x=-\frac{10}{\theta +3}\text{, }&\theta \neq -3\text{ and }arg(\frac{x\theta +10}{3})<\pi \end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{10}{\theta -3}\text{, }&\theta <3\\x=-\frac{10}{\theta +3}\text{, }&\theta >-3\end{matrix}\right.$$