Solve x^2+2^2+(-3)^2=0

$$x ^ { 2 } + 2 ^ { 2 } + ( - 3 ) ^ { 2 } = 0$$

Solve for x (complex solution)

$$x=-\sqrt{13}i\approx -0-3.605551275i$$

$$x=\sqrt{13}i\approx 3.605551275i$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$x^{2}+4+\left(-3\right)^{2}=0$$

Calculate -3 to the power of 2 and get 9.

$$x^{2}+4+9=0$$

Add 4 and 9 to get 13.

$$x^{2}+13=0$$

Subtract 13 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-13$$

The equation is now solved.

$$x=\sqrt{13}i x=-\sqrt{13}i$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$x^{2}+4+\left(-3\right)^{2}=0$$

Calculate -3 to the power of 2 and get 9.

$$x^{2}+4+9=0$$

Add 4 and 9 to get 13.

$$x^{2}+13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13}}{2}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52}}{2}$$

Take the square root of -52.

$$x=\frac{0±2\sqrt{13}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{13}i}{2} when ± is plus.

$$x=\sqrt{13}i$$

Now solve the equation x=\frac{0±2\sqrt{13}i}{2} when ± is minus.

$$x=-\sqrt{13}i$$

The equation is now solved.

$$x=\sqrt{13}i x=-\sqrt{13}i$$