Solve x^2+2^2+26=0

$${ x }^{ 2 } + { 2 }^{ 2 } +26=0$$

Solve for x (complex solution)

$$x=-\sqrt{30}i\approx -0-5.477225575i$$

$$x=\sqrt{30}i\approx 5.477225575i$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$x^{2}+4+26=0$$

Add 4 and 26 to get 30.

$$x^{2}+30=0$$

Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-30$$

The equation is now solved.

$$x=\sqrt{30}i x=-\sqrt{30}i$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$x^{2}+4+26=0$$

Add 4 and 26 to get 30.

$$x^{2}+30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 30}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 30}}{2}$$

Multiply -4 times 30.

$$x=\frac{0±\sqrt{-120}}{2}$$

Take the square root of -120.

$$x=\frac{0±2\sqrt{30}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{30}i}{2} when ± is plus.

$$x=\sqrt{30}i$$

Now solve the equation x=\frac{0±2\sqrt{30}i}{2} when ± is minus.

$$x=-\sqrt{30}i$$

The equation is now solved.

$$x=\sqrt{30}i x=-\sqrt{30}i$$