Solve 7x^2+3=0

$$7 { x }^{ 2 } +3=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{21}i}{7}\approx -0-0.654653671i$$

$$x=\frac{\sqrt{21}i}{7}\approx 0.654653671i$$

Steps by Finding Square Root

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$7x^{2}=-3$$

Divide both sides by 7.

$$x^{2}=-\frac{3}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{21}i}{7} x=-\frac{\sqrt{21}i}{7}$$

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.

$$7x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\times 3}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\times 3}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\times 3}}{2\times 7}$$

Multiply -28 times 3.

$$x=\frac{0±\sqrt{-84}}{2\times 7}$$

Take the square root of -84.

$$x=\frac{0±2\sqrt{21}i}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±2\sqrt{21}i}{14}$$

Now solve the equation x=\frac{0±2\sqrt{21}i}{14} when ± is plus.

$$x=\frac{\sqrt{21}i}{7}$$

Now solve the equation x=\frac{0±2\sqrt{21}i}{14} when ± is minus.

$$x=-\frac{\sqrt{21}i}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{21}i}{7} x=-\frac{\sqrt{21}i}{7}$$