Solve 36x^2+699=0

$$36 { x }^{ 2 } +699 = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{699}i}{6}\approx -0-4.406434689i$$

$$x=\frac{\sqrt{699}i}{6}\approx 4.406434689i$$

Steps by Finding Square Root

Subtract 699 from both sides. Anything subtracted from zero gives its negation.

$$36x^{2}=-699$$

Divide both sides by 36.

$$x^{2}=\frac{-699}{36}$$

Reduce the fraction \frac{-699}{36} to lowest terms by extracting and canceling out 3.

$$x^{2}=-\frac{233}{12}$$

The equation is now solved.

$$x=\frac{\sqrt{699}i}{6} x=-\frac{\sqrt{699}i}{6}$$

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.

$$36x^{2}+699=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and 699 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36\times 699}}{2\times 36}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 36\times 699}}{2\times 36}$$

Multiply -4 times 36.

$$x=\frac{0±\sqrt{-144\times 699}}{2\times 36}$$

Multiply -144 times 699.

$$x=\frac{0±\sqrt{-100656}}{2\times 36}$$

Take the square root of -100656.

$$x=\frac{0±12\sqrt{699}i}{2\times 36}$$

Multiply 2 times 36.

$$x=\frac{0±12\sqrt{699}i}{72}$$

Now solve the equation x=\frac{0±12\sqrt{699}i}{72} when ± is plus.

$$x=\frac{\sqrt{699}i}{6}$$

Now solve the equation x=\frac{0±12\sqrt{699}i}{72} when ± is minus.

$$x=-\frac{\sqrt{699}i}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{699}i}{6} x=-\frac{\sqrt{699}i}{6}$$