Solve 7x^2+6=-33

$$7 x ^ { 2 } + 6 = - 33$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{273}i}{7}\approx -0-2.360387377i$$

$$x=\frac{\sqrt{273}i}{7}\approx 2.360387377i$$

Steps by Finding Square Root

Subtract 6 from both sides.

$$7x^{2}=-33-6$$

Subtract 6 from -33 to get -39.

$$7x^{2}=-39$$

Divide both sides by 7.

$$x^{2}=-\frac{39}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{273}i}{7} x=-\frac{\sqrt{273}i}{7}$$

Steps Using the Quadratic Formula

Add 33 to both sides.

$$7x^{2}+6+33=0$$

Add 6 and 33 to get 39.

$$7x^{2}+39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and 39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\times 39}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\times 39}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\times 39}}{2\times 7}$$

Multiply -28 times 39.

$$x=\frac{0±\sqrt{-1092}}{2\times 7}$$

Take the square root of -1092.

$$x=\frac{0±2\sqrt{273}i}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±2\sqrt{273}i}{14}$$

Now solve the equation x=\frac{0±2\sqrt{273}i}{14} when ± is plus.

$$x=\frac{\sqrt{273}i}{7}$$

Now solve the equation x=\frac{0±2\sqrt{273}i}{14} when ± is minus.

$$x=-\frac{\sqrt{273}i}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{273}i}{7} x=-\frac{\sqrt{273}i}{7}$$