Solve 5y*4y=31

$$5 y \times 4 y = 31$$

Solve for y

$$y = \frac{\sqrt{155}}{10} \approx 1.24498996$$

$$y = -\frac{\sqrt{155}}{10} \approx -1.24498996$$

Steps by Finding Square Root

Multiply y and y to get y^{2}.

$$5y^{2}\times 4=31$$

Multiply 5 and 4 to get 20.

$$20y^{2}=31$$

Divide both sides by 20.

$$y^{2}=\frac{31}{20}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{155}}{10} y=-\frac{\sqrt{155}}{10}$$

Steps Using the Quadratic Formula

Multiply y and y to get y^{2}.

$$5y^{2}\times 4=31$$

Multiply 5 and 4 to get 20.

$$20y^{2}=31$$

Subtract 31 from both sides.

$$20y^{2}-31=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -31 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 20\left(-31\right)}}{2\times 20}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 20\left(-31\right)}}{2\times 20}$$

Multiply -4 times 20.

$$y=\frac{0±\sqrt{-80\left(-31\right)}}{2\times 20}$$

Multiply -80 times -31.

$$y=\frac{0±\sqrt{2480}}{2\times 20}$$

Take the square root of 2480.

$$y=\frac{0±4\sqrt{155}}{2\times 20}$$

Multiply 2 times 20.

$$y=\frac{0±4\sqrt{155}}{40}$$

Now solve the equation y=\frac{0±4\sqrt{155}}{40} when ± is plus.

$$y=\frac{\sqrt{155}}{10}$$

Now solve the equation y=\frac{0±4\sqrt{155}}{40} when ± is minus.

$$y=-\frac{\sqrt{155}}{10}$$

The equation is now solved.

$$y=\frac{\sqrt{155}}{10} y=-\frac{\sqrt{155}}{10}$$