Solve (0^3+6D^2+110+6)4=0

$$( 0 ^ { 3 } + 6 D ^ { 2 } + 110 + 6 ) 4 = 0$$

Solve for D

$$D=-\frac{\sqrt{174}i}{3}\approx -0-4.396968653i$$

$$D=\frac{\sqrt{174}i}{3}\approx 4.396968653i$$

Steps by Finding Square Root

Divide both sides by 4. Zero divided by any non-zero number gives zero.

$$0^{3}+6D^{2}+110+6=0$$

Calculate 0 to the power of 3 and get 0.

$$0+6D^{2}+110+6=0$$

Add 0 and 110 to get 110.

$$110+6D^{2}+6=0$$

Add 110 and 6 to get 116.

$$116+6D^{2}=0$$

Subtract 116 from both sides. Anything subtracted from zero gives its negation.

$$6D^{2}=-116$$

Divide both sides by 6.

$$D^{2}=\frac{-116}{6}$$

Reduce the fraction \frac{-116}{6} to lowest terms by extracting and canceling out 2.

$$D^{2}=-\frac{58}{3}$$

The equation is now solved.

$$D=\frac{\sqrt{174}i}{3} D=-\frac{\sqrt{174}i}{3}$$

Steps Using the Quadratic Formula

Divide both sides by 4. Zero divided by any non-zero number gives zero.

$$0^{3}+6D^{2}+110+6=0$$

Calculate 0 to the power of 3 and get 0.

$$0+6D^{2}+110+6=0$$

Add 0 and 110 to get 110.

$$110+6D^{2}+6=0$$

Add 110 and 6 to get 116.

$$116+6D^{2}=0$$

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.

$$6D^{2}+116=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 116 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$D=\frac{0±\sqrt{0^{2}-4\times 6\times 116}}{2\times 6}$$

Square 0.

$$D=\frac{0±\sqrt{-4\times 6\times 116}}{2\times 6}$$

Multiply -4 times 6.

$$D=\frac{0±\sqrt{-24\times 116}}{2\times 6}$$

Multiply -24 times 116.

$$D=\frac{0±\sqrt{-2784}}{2\times 6}$$

Take the square root of -2784.

$$D=\frac{0±4\sqrt{174}i}{2\times 6}$$

Multiply 2 times 6.

$$D=\frac{0±4\sqrt{174}i}{12}$$

Now solve the equation D=\frac{0±4\sqrt{174}i}{12} when ± is plus.

$$D=\frac{\sqrt{174}i}{3}$$

Now solve the equation D=\frac{0±4\sqrt{174}i}{12} when ± is minus.

$$D=-\frac{\sqrt{174}i}{3}$$

The equation is now solved.

$$D=\frac{\sqrt{174}i}{3} D=-\frac{\sqrt{174}i}{3}$$