Solve sqrt{4}(4)=n^2-5/2

$$\sqrt { 4 } ( 4 ) = \frac { n ^ { 2 } - 5 } { 2 }$$

Solve for n

$$n=\sqrt{21}\approx 4.582575695$$

$$n=-\sqrt{21}\approx -4.582575695$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$2\sqrt{4}\times 4=n^{2}-5$$

Calculate the square root of 4 and get 2.

$$2\times 2\times 4=n^{2}-5$$

Multiply 2 and 2 to get 4.

$$4\times 4=n^{2}-5$$

Multiply 4 and 4 to get 16.

$$16=n^{2}-5$$

Swap sides so that all variable terms are on the left hand side.

$$n^{2}-5=16$$

Add 5 to both sides.

$$n^{2}=16+5$$

Add 16 and 5 to get 21.

$$n^{2}=21$$

Take the square root of both sides of the equation.

$$n=\sqrt{21} n=-\sqrt{21}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$2\sqrt{4}\times 4=n^{2}-5$$

Calculate the square root of 4 and get 2.

$$2\times 2\times 4=n^{2}-5$$

Multiply 2 and 2 to get 4.

$$4\times 4=n^{2}-5$$

Multiply 4 and 4 to get 16.

$$16=n^{2}-5$$

Swap sides so that all variable terms are on the left hand side.

$$n^{2}-5=16$$

Subtract 16 from both sides.

$$n^{2}-5-16=0$$

Subtract 16 from -5 to get -21.

$$n^{2}-21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-21\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-21\right)}}{2}$$

Multiply -4 times -21.

$$n=\frac{0±\sqrt{84}}{2}$$

Take the square root of 84.

$$n=\frac{0±2\sqrt{21}}{2}$$

Now solve the equation n=\frac{0±2\sqrt{21}}{2} when ± is plus.

$$n=\sqrt{21}$$

Now solve the equation n=\frac{0±2\sqrt{21}}{2} when ± is minus.

$$n=-\sqrt{21}$$

The equation is now solved.

$$n=\sqrt{21} n=-\sqrt{21}$$