Solve 6n^2+4=298

$$6 n ^ { 2 } + 4 = 298$$

Solve for n

$$n=7$$

$$n=-7$$

Steps Using Difference of Squares

Subtract 298 from both sides.

$$6n^{2}+4-298=0$$

Subtract 298 from 4 to get -294.

$$6n^{2}-294=0$$

Divide both sides by 6.

$$n^{2}-49=0$$

Consider n^{2}-49. Rewrite n^{2}-49 as n^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-7\right)\left(n+7\right)=0$$

To find equation solutions, solve n-7=0 and n+7=0.

$$n=7 n=-7$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$6n^{2}=298-4$$

Subtract 4 from 298 to get 294.

$$6n^{2}=294$$

Divide both sides by 6.

$$n^{2}=\frac{294}{6}$$

Divide 294 by 6 to get 49.

$$n^{2}=49$$

Take the square root of both sides of the equation.

$$n=7 n=-7$$

Steps Using the Quadratic Formula

Subtract 298 from both sides.

$$6n^{2}+4-298=0$$

Subtract 298 from 4 to get -294.

$$6n^{2}-294=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -294 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 6\left(-294\right)}}{2\times 6}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 6\left(-294\right)}}{2\times 6}$$

Multiply -4 times 6.

$$n=\frac{0±\sqrt{-24\left(-294\right)}}{2\times 6}$$

Multiply -24 times -294.

$$n=\frac{0±\sqrt{7056}}{2\times 6}$$

Take the square root of 7056.

$$n=\frac{0±84}{2\times 6}$$

Multiply 2 times 6.

$$n=\frac{0±84}{12}$$

Now solve the equation n=\frac{0±84}{12} when ± is plus. Divide 84 by 12.

$$n=7$$

Now solve the equation n=\frac{0±84}{12} when ± is minus. Divide -84 by 12.

$$n=-7$$

The equation is now solved.

$$n=7 n=-7$$