Solve 1000+x^2=500

$$1000 + x ^ { 2 } = 500$$

Solve for x (complex solution)

$$x=-10\sqrt{5}i\approx -0-22.360679775i$$

$$x=10\sqrt{5}i\approx 22.360679775i$$

Steps by Finding Square Root

Subtract 1000 from both sides.

$$x^{2}=500-1000$$

Subtract 1000 from 500 to get -500.

$$x^{2}=-500$$

The equation is now solved.

$$x=10\sqrt{5}i x=-10\sqrt{5}i$$

Steps Using the Quadratic Formula

Subtract 500 from both sides.

$$1000+x^{2}-500=0$$

Subtract 500 from 1000 to get 500.

$$500+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 500}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 500}}{2}$$

Multiply -4 times 500.

$$x=\frac{0±\sqrt{-2000}}{2}$$

Take the square root of -2000.

$$x=\frac{0±20\sqrt{5}i}{2}$$

Now solve the equation x=\frac{0±20\sqrt{5}i}{2} when ± is plus.

$$x=10\sqrt{5}i$$

Now solve the equation x=\frac{0±20\sqrt{5}i}{2} when ± is minus.

$$x=-10\sqrt{5}i$$

The equation is now solved.

$$x=10\sqrt{5}i x=-10\sqrt{5}i$$