Solve 4+124x^2=0

$$4+124 { x }^{ 2 } =0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{31}i}{31}\approx -0-0.179605302i$$

$$x=\frac{\sqrt{31}i}{31}\approx 0.179605302i$$

Steps by Finding Square Root

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$124x^{2}=-4$$

Divide both sides by 124.

$$x^{2}=\frac{-4}{124}$$

Reduce the fraction \frac{-4}{124} to lowest terms by extracting and canceling out 4.

$$x^{2}=-\frac{1}{31}$$

The equation is now solved.

$$x=\frac{\sqrt{31}i}{31} x=-\frac{\sqrt{31}i}{31}$$

Steps Using the Quadratic Formula

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.

$$124x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 124 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 124\times 4}}{2\times 124}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 124\times 4}}{2\times 124}$$

Multiply -4 times 124.

$$x=\frac{0±\sqrt{-496\times 4}}{2\times 124}$$

Multiply -496 times 4.

$$x=\frac{0±\sqrt{-1984}}{2\times 124}$$

Take the square root of -1984.

$$x=\frac{0±8\sqrt{31}i}{2\times 124}$$

Multiply 2 times 124.

$$x=\frac{0±8\sqrt{31}i}{248}$$

Now solve the equation x=\frac{0±8\sqrt{31}i}{248} when ± is plus.

$$x=\frac{\sqrt{31}i}{31}$$

Now solve the equation x=\frac{0±8\sqrt{31}i}{248} when ± is minus.

$$x=-\frac{\sqrt{31}i}{31}$$

The equation is now solved.

$$x=\frac{\sqrt{31}i}{31} x=-\frac{\sqrt{31}i}{31}$$