Solve x^2=5-5^2

$${ x }^{ 2 } =5- { 5 }^{ 2 }$$

Solve for x (complex solution)

$$x=-2\sqrt{5}i\approx -0-4.472135955i$$

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

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$x^{2}=5-25$$

Subtract 25 from 5 to get -20.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$x^{2}=5-25$$

Subtract 25 from 5 to get -20.

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

Add 20 to 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}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20}}{2}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80}}{2}$$

Take the square root of -80.

$$x=\frac{0±4\sqrt{5}i}{2}$$

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

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

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

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

The equation is now solved.

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