Solve 3n^2+7=301

$$3 n ^ { 2 } + 7 = 301$$

Solve for n

$$n=7\sqrt{2}\approx 9.899494937$$

$$n=-7\sqrt{2}\approx -9.899494937$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$3n^{2}=301-7$$

Subtract 7 from 301 to get 294.

$$3n^{2}=294$$

Divide both sides by 3.

$$n^{2}=\frac{294}{3}$$

Divide 294 by 3 to get 98.

$$n^{2}=98$$

Take the square root of both sides of the equation.

$$n=7\sqrt{2} n=-7\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 301 from both sides.

$$3n^{2}+7-301=0$$

Subtract 301 from 7 to get -294.

$$3n^{2}-294=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -294 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 3\left(-294\right)}}{2\times 3}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 3\left(-294\right)}}{2\times 3}$$

Multiply -4 times 3.

$$n=\frac{0±\sqrt{-12\left(-294\right)}}{2\times 3}$$

Multiply -12 times -294.

$$n=\frac{0±\sqrt{3528}}{2\times 3}$$

Take the square root of 3528.

$$n=\frac{0±42\sqrt{2}}{2\times 3}$$

Multiply 2 times 3.

$$n=\frac{0±42\sqrt{2}}{6}$$

Now solve the equation n=\frac{0±42\sqrt{2}}{6} when ± is plus.

$$n=7\sqrt{2}$$

Now solve the equation n=\frac{0±42\sqrt{2}}{6} when ± is minus.

$$n=-7\sqrt{2}$$

The equation is now solved.

$$n=7\sqrt{2} n=-7\sqrt{2}$$