Solve 5x^2+33=3

$$5 x ^ { 2 } + 33 = 3$$

Solve for x (complex solution)

$$x=-\sqrt{6}i\approx -0-2.449489743i$$

$$x=\sqrt{6}i\approx 2.449489743i$$

Steps by Finding Square Root

Subtract 33 from both sides.

$$5x^{2}=3-33$$

Subtract 33 from 3 to get -30.

$$5x^{2}=-30$$

Divide both sides by 5.

$$x^{2}=\frac{-30}{5}$$

Divide -30 by 5 to get -6.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$5x^{2}+33-3=0$$

Subtract 3 from 33 to get 30.

$$5x^{2}+30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 30}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 30}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 30}}{2\times 5}$$

Multiply -20 times 30.

$$x=\frac{0±\sqrt{-600}}{2\times 5}$$

Take the square root of -600.

$$x=\frac{0±10\sqrt{6}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±10\sqrt{6}i}{10}$$

Now solve the equation x=\frac{0±10\sqrt{6}i}{10} when ± is plus.

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

Now solve the equation x=\frac{0±10\sqrt{6}i}{10} when ± is minus.

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

The equation is now solved.

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