Solve 33x^2-55x^2-1*5=1

$$33 x ^ { 2 } - 55 x ^ { 2 } - 1 \cdot 5 = 1$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{33}i}{11}\approx -0-0.522232968i$$

$$x=\frac{\sqrt{33}i}{11}\approx 0.522232968i$$

Steps by Finding Square Root

Combine 33x^{2} and -55x^{2} to get -22x^{2}.

$$-22x^{2}-1\times 5=1$$

Multiply 1 and 5 to get 5.

$$-22x^{2}-5=1$$

Add 5 to both sides.

$$-22x^{2}=1+5$$

Add 1 and 5 to get 6.

$$-22x^{2}=6$$

Divide both sides by -22.

$$x^{2}=\frac{6}{-22}$$

Reduce the fraction \frac{6}{-22} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{3}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{33}i}{11} x=-\frac{\sqrt{33}i}{11}$$

Steps Using the Quadratic Formula

Combine 33x^{2} and -55x^{2} to get -22x^{2}.

$$-22x^{2}-1\times 5=1$$

Multiply 1 and 5 to get 5.

$$-22x^{2}-5=1$$

Subtract 1 from both sides.

$$-22x^{2}-5-1=0$$

Subtract 1 from -5 to get -6.

$$-22x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -22 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-22\right)\left(-6\right)}}{2\left(-22\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-22\right)\left(-6\right)}}{2\left(-22\right)}$$

Multiply -4 times -22.

$$x=\frac{0±\sqrt{88\left(-6\right)}}{2\left(-22\right)}$$

Multiply 88 times -6.

$$x=\frac{0±\sqrt{-528}}{2\left(-22\right)}$$

Take the square root of -528.

$$x=\frac{0±4\sqrt{33}i}{2\left(-22\right)}$$

Multiply 2 times -22.

$$x=\frac{0±4\sqrt{33}i}{-44}$$

Now solve the equation x=\frac{0±4\sqrt{33}i}{-44} when ± is plus.

$$x=-\frac{\sqrt{33}i}{11}$$

Now solve the equation x=\frac{0±4\sqrt{33}i}{-44} when ± is minus.

$$x=\frac{\sqrt{33}i}{11}$$

The equation is now solved.

$$x=-\frac{\sqrt{33}i}{11} x=\frac{\sqrt{33}i}{11}$$