Solve 10n^2+2=292

$$10 n ^ { 2 } + 2 = 292$$

Solve for n

$$n=\sqrt{29}\approx 5.385164807$$

$$n=-\sqrt{29}\approx -5.385164807$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$10n^{2}=292-2$$

Subtract 2 from 292 to get 290.

$$10n^{2}=290$$

Divide both sides by 10.

$$n^{2}=\frac{290}{10}$$

Divide 290 by 10 to get 29.

$$n^{2}=29$$

Take the square root of both sides of the equation.

$$n=\sqrt{29} n=-\sqrt{29}$$

Steps Using the Quadratic Formula

Subtract 292 from both sides.

$$10n^{2}+2-292=0$$

Subtract 292 from 2 to get -290.

$$10n^{2}-290=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -290 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 10\left(-290\right)}}{2\times 10}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 10\left(-290\right)}}{2\times 10}$$

Multiply -4 times 10.

$$n=\frac{0±\sqrt{-40\left(-290\right)}}{2\times 10}$$

Multiply -40 times -290.

$$n=\frac{0±\sqrt{11600}}{2\times 10}$$

Take the square root of 11600.

$$n=\frac{0±20\sqrt{29}}{2\times 10}$$

Multiply 2 times 10.

$$n=\frac{0±20\sqrt{29}}{20}$$

Now solve the equation n=\frac{0±20\sqrt{29}}{20} when ± is plus.

$$n=\sqrt{29}$$

Now solve the equation n=\frac{0±20\sqrt{29}}{20} when ± is minus.

$$n=-\sqrt{29}$$

The equation is now solved.

$$n=\sqrt{29} n=-\sqrt{29}$$