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

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

Solve for x

$$x=2\sqrt{5}\approx 4.472135955$$

$$x=-2\sqrt{5}\approx -4.472135955$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}=4+16$$

Add 4 and 16 to get 20.

$$x^{2}=20$$

Take the square root of both sides of the equation.

$$x=2\sqrt{5} x=-2\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}=4+16$$

Add 4 and 16 to get 20.

$$x^{2}=20$$

Subtract 20 from both sides.

$$x^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-20\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-20\right)}}{2}$$

Multiply -4 times -20.

$$x=\frac{0±\sqrt{80}}{2}$$

Take the square root of 80.

$$x=\frac{0±4\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{2} when ± is plus.

$$x=2\sqrt{5}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{2} when ± is minus.

$$x=-2\sqrt{5}$$

The equation is now solved.

$$x=2\sqrt{5} x=-2\sqrt{5}$$