Solve x^2+2=5^2+4^2

$$x ^ { 2 } + 2 = 5 ^ { 2 } + 4 ^ { 2 }$$

Solve for x

$$x=\sqrt{39}\approx 6.244997998$$

$$x=-\sqrt{39}\approx -6.244997998$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$x^{2}+2=25+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}+2=25+16$$

Add 25 and 16 to get 41.

$$x^{2}+2=41$$

Subtract 2 from both sides.

$$x^{2}=41-2$$

Subtract 2 from 41 to get 39.

$$x^{2}=39$$

Take the square root of both sides of the equation.

$$x=\sqrt{39} x=-\sqrt{39}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$x^{2}+2=25+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}+2=25+16$$

Add 25 and 16 to get 41.

$$x^{2}+2=41$$

Subtract 41 from both sides.

$$x^{2}+2-41=0$$

Subtract 41 from 2 to get -39.

$$x^{2}-39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-39\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-39\right)}}{2}$$

Multiply -4 times -39.

$$x=\frac{0±\sqrt{156}}{2}$$

Take the square root of 156.

$$x=\frac{0±2\sqrt{39}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{39}}{2} when ± is plus.

$$x=\sqrt{39}$$

Now solve the equation x=\frac{0±2\sqrt{39}}{2} when ± is minus.

$$x=-\sqrt{39}$$

The equation is now solved.

$$x=\sqrt{39} x=-\sqrt{39}$$