Solve 5n^2+5=45

$$5 n ^ { 2 } + 5 = 45$$

Solve for n

$$n=2\sqrt{2}\approx 2.828427125$$

$$n=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$5n^{2}=45-5$$

Subtract 5 from 45 to get 40.

$$5n^{2}=40$$

Divide both sides by 5.

$$n^{2}=\frac{40}{5}$$

Divide 40 by 5 to get 8.

$$n^{2}=8$$

Take the square root of both sides of the equation.

$$n=2\sqrt{2} n=-2\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 45 from both sides.

$$5n^{2}+5-45=0$$

Subtract 45 from 5 to get -40.

$$5n^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 5\left(-40\right)}}{2\times 5}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 5\left(-40\right)}}{2\times 5}$$

Multiply -4 times 5.

$$n=\frac{0±\sqrt{-20\left(-40\right)}}{2\times 5}$$

Multiply -20 times -40.

$$n=\frac{0±\sqrt{800}}{2\times 5}$$

Take the square root of 800.

$$n=\frac{0±20\sqrt{2}}{2\times 5}$$

Multiply 2 times 5.

$$n=\frac{0±20\sqrt{2}}{10}$$

Now solve the equation n=\frac{0±20\sqrt{2}}{10} when ± is plus.

$$n=2\sqrt{2}$$

Now solve the equation n=\frac{0±20\sqrt{2}}{10} when ± is minus.

$$n=-2\sqrt{2}$$

The equation is now solved.

$$n=2\sqrt{2} n=-2\sqrt{2}$$