Solve 11/50y=?/100y^3

$$\frac { 11 } { 50 y } = \frac { ? } { 100 y ^ { 3 } }$$

Solve for y

$$y=\frac{\sqrt{22}}{22}\approx 0.213200716$$

$$y=-\frac{\sqrt{22}}{22}\approx -0.213200716$$

Steps by Finding Square Root

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100y^{3}, the least common multiple of 50y,100y^{3}.

$$2y^{2}\times 11=1$$

Multiply 2 and 11 to get 22.

$$22y^{2}=1$$

Divide both sides by 22.

$$y^{2}=\frac{1}{22}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{22}}{22} y=-\frac{\sqrt{22}}{22}$$

Steps Using the Quadratic Formula

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100y^{3}, the least common multiple of 50y,100y^{3}.

$$2y^{2}\times 11=1$$

Multiply 2 and 11 to get 22.

$$22y^{2}=1$$

Subtract 1 from both sides.

$$22y^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 22 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 22\left(-1\right)}}{2\times 22}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 22\left(-1\right)}}{2\times 22}$$

Multiply -4 times 22.

$$y=\frac{0±\sqrt{-88\left(-1\right)}}{2\times 22}$$

Multiply -88 times -1.

$$y=\frac{0±\sqrt{88}}{2\times 22}$$

Take the square root of 88.

$$y=\frac{0±2\sqrt{22}}{2\times 22}$$

Multiply 2 times 22.

$$y=\frac{0±2\sqrt{22}}{44}$$

Now solve the equation y=\frac{0±2\sqrt{22}}{44} when ± is plus.

$$y=\frac{\sqrt{22}}{22}$$

Now solve the equation y=\frac{0±2\sqrt{22}}{44} when ± is minus.

$$y=-\frac{\sqrt{22}}{22}$$

The equation is now solved.

$$y=\frac{\sqrt{22}}{22} y=-\frac{\sqrt{22}}{22}$$