Solve 5y^2+1=8

$$5 y ^ { 2 } + 1 = 8$$

Solve for y

$$y = \frac{\sqrt{35}}{5} \approx 1.183215957$$

$$y = -\frac{\sqrt{35}}{5} \approx -1.183215957$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$5y^{2}=8-1$$

Subtract 1 from 8 to get 7.

$$5y^{2}=7$$

Divide both sides by 5.

$$y^{2}=\frac{7}{5}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{35}}{5} y=-\frac{\sqrt{35}}{5}$$

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$5y^{2}+1-8=0$$

Subtract 8 from 1 to get -7.

$$5y^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 5\left(-7\right)}}{2\times 5}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 5\left(-7\right)}}{2\times 5}$$

Multiply -4 times 5.

$$y=\frac{0±\sqrt{-20\left(-7\right)}}{2\times 5}$$

Multiply -20 times -7.

$$y=\frac{0±\sqrt{140}}{2\times 5}$$

Take the square root of 140.

$$y=\frac{0±2\sqrt{35}}{2\times 5}$$

Multiply 2 times 5.

$$y=\frac{0±2\sqrt{35}}{10}$$

Now solve the equation y=\frac{0±2\sqrt{35}}{10} when ± is plus.

$$y=\frac{\sqrt{35}}{5}$$

Now solve the equation y=\frac{0±2\sqrt{35}}{10} when ± is minus.

$$y=-\frac{\sqrt{35}}{5}$$

The equation is now solved.

$$y=\frac{\sqrt{35}}{5} y=-\frac{\sqrt{35}}{5}$$