Solve 10n^2-10=470

$$10 n ^ { 2 } - 10 = 470$$

Solve for n

$$n=4\sqrt{3}\approx 6.92820323$$

$$n=-4\sqrt{3}\approx -6.92820323$$

Steps by Finding Square Root

Add 10 to both sides.

$$10n^{2}=470+10$$

Add 470 and 10 to get 480.

$$10n^{2}=480$$

Divide both sides by 10.

$$n^{2}=\frac{480}{10}$$

Divide 480 by 10 to get 48.

$$n^{2}=48$$

Take the square root of both sides of the equation.

$$n=4\sqrt{3} n=-4\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 470 from both sides.

$$10n^{2}-10-470=0$$

Subtract 470 from -10 to get -480.

$$10n^{2}-480=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -480 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 10\left(-480\right)}}{2\times 10}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 10\left(-480\right)}}{2\times 10}$$

Multiply -4 times 10.

$$n=\frac{0±\sqrt{-40\left(-480\right)}}{2\times 10}$$

Multiply -40 times -480.

$$n=\frac{0±\sqrt{19200}}{2\times 10}$$

Take the square root of 19200.

$$n=\frac{0±80\sqrt{3}}{2\times 10}$$

Multiply 2 times 10.

$$n=\frac{0±80\sqrt{3}}{20}$$

Now solve the equation n=\frac{0±80\sqrt{3}}{20} when ± is plus.

$$n=4\sqrt{3}$$

Now solve the equation n=\frac{0±80\sqrt{3}}{20} when ± is minus.

$$n=-4\sqrt{3}$$

The equation is now solved.

$$n=4\sqrt{3} n=-4\sqrt{3}$$