Solve f(r_{11})y=frac{sqrt[3]{x}-4x^2-16}{sqrt{2}}

$$f ( r _ { 11 } ) y = \frac { \sqrt[ 3 ] { x } - 4 x ^ { 2 } - 16 } { \sqrt { 2 } }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{\sqrt{2}\left(4x^{2}-\sqrt[3]{x}+16\right)}{2r_{11}y}\text{, }&y\neq 0\text{ and }r_{11}\neq 0\\f\in \mathrm{C}\text{, }&4x^{2}-\sqrt[3]{x}+16=0\text{ and }\left(y=0\text{ or }r_{11}=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt[3]{x}-4x^{2}-16}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{2}$$

Use the distributive property to multiply \sqrt[3]{x}-4x^{2}-16 by \sqrt{2}.

$$fr_{11}y=\frac{\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}}{2}$$

Multiply both sides of the equation by 2.

$$2fr_{11}y=\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}$$

The equation is in standard form.

$$2r_{11}yf=-4\sqrt{2}x^{2}+\sqrt{2}\sqrt[3]{x}-16\sqrt{2}$$

Divide both sides by 2r_{11}y.

$$\frac{2r_{11}yf}{2r_{11}y}=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2r_{11}y}$$

Dividing by 2r_{11}y undoes the multiplication by 2r_{11}y.

$$f=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2r_{11}y}$$

Solve for r_11 (complex solution)

$$\left\{\begin{matrix}r_{11}=-\frac{\sqrt{2}\left(4x^{2}-\sqrt[3]{x}+16\right)}{2fy}\text{, }&y\neq 0\text{ and }f\neq 0\\r_{11}\in \mathrm{C}\text{, }&4x^{2}-\sqrt[3]{x}+16=0\text{ and }\left(y=0\text{ or }f=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt[3]{x}-4x^{2}-16}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{2}$$

Use the distributive property to multiply \sqrt[3]{x}-4x^{2}-16 by \sqrt{2}.

$$fr_{11}y=\frac{\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}}{2}$$

Multiply both sides of the equation by 2.

$$2fr_{11}y=\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}$$

The equation is in standard form.

$$2fyr_{11}=-4\sqrt{2}x^{2}+\sqrt{2}\sqrt[3]{x}-16\sqrt{2}$$

Divide both sides by 2fy.

$$\frac{2fyr_{11}}{2fy}=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2fy}$$

Dividing by 2fy undoes the multiplication by 2fy.

$$r_{11}=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2fy}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{\sqrt{2}\left(4x^{2}-\sqrt[3]{x}+16\right)}{2r_{11}y}\text{, }&y\neq 0\text{ and }r_{11}\neq 0\\f\in \mathrm{R}\text{, }&4x^{2}-\sqrt[3]{x}+16=0\text{ and }\left(y=0\text{ or }r_{11}=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt[3]{x}-4x^{2}-16}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{2}$$

Use the distributive property to multiply \sqrt[3]{x}-4x^{2}-16 by \sqrt{2}.

$$fr_{11}y=\frac{\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}}{2}$$

Multiply both sides of the equation by 2.

$$2fr_{11}y=\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}$$

The equation is in standard form.

$$2r_{11}yf=-4\sqrt{2}x^{2}+\sqrt{2}\sqrt[3]{x}-16\sqrt{2}$$

Divide both sides by 2r_{11}y.

$$\frac{2r_{11}yf}{2r_{11}y}=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2r_{11}y}$$

Dividing by 2r_{11}y undoes the multiplication by 2r_{11}y.

$$f=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2r_{11}y}$$

Solve for r_11

$$\left\{\begin{matrix}r_{11}=-\frac{\sqrt{2}\left(4x^{2}-\sqrt[3]{x}+16\right)}{2fy}\text{, }&y\neq 0\text{ and }f\neq 0\\r_{11}\in \mathrm{R}\text{, }&4x^{2}-\sqrt[3]{x}+16=0\text{ and }\left(y=0\text{ or }f=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt[3]{x}-4x^{2}-16}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$fr_{11}y=\frac{\left(\sqrt[3]{x}-4x^{2}-16\right)\sqrt{2}}{2}$$

Use the distributive property to multiply \sqrt[3]{x}-4x^{2}-16 by \sqrt{2}.

$$fr_{11}y=\frac{\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}}{2}$$

Multiply both sides of the equation by 2.

$$2fr_{11}y=\sqrt[3]{x}\sqrt{2}-4x^{2}\sqrt{2}-16\sqrt{2}$$

The equation is in standard form.

$$2fyr_{11}=-4\sqrt{2}x^{2}+\sqrt{2}\sqrt[3]{x}-16\sqrt{2}$$

Divide both sides by 2fy.

$$\frac{2fyr_{11}}{2fy}=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2fy}$$

Dividing by 2fy undoes the multiplication by 2fy.

$$r_{11}=\frac{\sqrt{2}\left(-4x^{2}+\sqrt[3]{x}-16\right)}{2fy}$$