Solve left(1+500right)x^2+10=0

$$\left( 1+500 \right) { x }^{ 2 } +10=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{5010}i}{501}\approx -0-0.141280147i$$

$$x=\frac{\sqrt{5010}i}{501}\approx 0.141280147i$$

Steps by Finding Square Root

Add 1 and 500 to get 501.

$$501x^{2}+10=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$501x^{2}=-10$$

Divide both sides by 501.

$$x^{2}=-\frac{10}{501}$$

The equation is now solved.

$$x=\frac{\sqrt{5010}i}{501} x=-\frac{\sqrt{5010}i}{501}$$

Steps Using the Quadratic Formula

Add 1 and 500 to get 501.

$$501x^{2}+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 501 for a, 0 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 501\times 10}}{2\times 501}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 501\times 10}}{2\times 501}$$

Multiply -4 times 501.

$$x=\frac{0±\sqrt{-2004\times 10}}{2\times 501}$$

Multiply -2004 times 10.

$$x=\frac{0±\sqrt{-20040}}{2\times 501}$$

Take the square root of -20040.

$$x=\frac{0±2\sqrt{5010}i}{2\times 501}$$

Multiply 2 times 501.

$$x=\frac{0±2\sqrt{5010}i}{1002}$$

Now solve the equation x=\frac{0±2\sqrt{5010}i}{1002} when ± is plus.

$$x=\frac{\sqrt{5010}i}{501}$$

Now solve the equation x=\frac{0±2\sqrt{5010}i}{1002} when ± is minus.

$$x=-\frac{\sqrt{5010}i}{501}$$

The equation is now solved.

$$x=\frac{\sqrt{5010}i}{501} x=-\frac{\sqrt{5010}i}{501}$$