Solve x^2-200+3600=0

$$x ^ { 2 } - 200 + 3600 = 0$$

Solve for x (complex solution)

$$x=-10\sqrt{34}i\approx -0-58.309518948i$$

$$x=10\sqrt{34}i\approx 58.309518948i$$

Steps by Finding Square Root

Add -200 and 3600 to get 3400.

$$x^{2}+3400=0$$

Subtract 3400 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-3400$$

The equation is now solved.

$$x=10\sqrt{34}i x=-10\sqrt{34}i$$

Steps Using the Quadratic Formula

Add -200 and 3600 to get 3400.

$$x^{2}+3400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 3400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3400}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3400}}{2}$$

Multiply -4 times 3400.

$$x=\frac{0±\sqrt{-13600}}{2}$$

Take the square root of -13600.

$$x=\frac{0±20\sqrt{34}i}{2}$$

Now solve the equation x=\frac{0±20\sqrt{34}i}{2} when ± is plus.

$$x=10\sqrt{34}i$$

Now solve the equation x=\frac{0±20\sqrt{34}i}{2} when ± is minus.

$$x=-10\sqrt{34}i$$

The equation is now solved.

$$x=10\sqrt{34}i x=-10\sqrt{34}i$$