Solve -4/5a^2-9/20a^2=1

$$- \frac { 4 } { 5 a ^ { 2 } } - \frac { 9 } { 20 a ^ { 2 } } = 1$$

Solve for a

$$a=-\frac{\sqrt{5}i}{2}\approx -0-1.118033989i$$

$$a=\frac{\sqrt{5}i}{2}\approx 1.118033989i$$

Steps by Finding Square Root

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 20a^{2}, the least common multiple of 5a^{2},20a^{2}.

$$-4\times 4-9=20a^{2}$$

Multiply -4 and 4 to get -16.

$$-16-9=20a^{2}$$

Subtract 9 from -16 to get -25.

$$-25=20a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$20a^{2}=-25$$

Divide both sides by 20.

$$a^{2}=\frac{-25}{20}$$

Reduce the fraction \frac{-25}{20} to lowest terms by extracting and canceling out 5.

$$a^{2}=-\frac{5}{4}$$

The equation is now solved.

$$a=\frac{\sqrt{5}i}{2} a=-\frac{\sqrt{5}i}{2}$$

Steps Using the Quadratic Formula

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 20a^{2}, the least common multiple of 5a^{2},20a^{2}.

$$-4\times 4-9=20a^{2}$$

Multiply -4 and 4 to get -16.

$$-16-9=20a^{2}$$

Subtract 9 from -16 to get -25.

$$-25=20a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$20a^{2}=-25$$

Add 25 to both sides.

$$20a^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 20\times 25}}{2\times 20}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 20\times 25}}{2\times 20}$$

Multiply -4 times 20.

$$a=\frac{0±\sqrt{-80\times 25}}{2\times 20}$$

Multiply -80 times 25.

$$a=\frac{0±\sqrt{-2000}}{2\times 20}$$

Take the square root of -2000.

$$a=\frac{0±20\sqrt{5}i}{2\times 20}$$

Multiply 2 times 20.

$$a=\frac{0±20\sqrt{5}i}{40}$$

Now solve the equation a=\frac{0±20\sqrt{5}i}{40} when ± is plus.

$$a=\frac{\sqrt{5}i}{2}$$

Now solve the equation a=\frac{0±20\sqrt{5}i}{40} when ± is minus.

$$a=-\frac{\sqrt{5}i}{2}$$

The equation is now solved.

$$a=\frac{\sqrt{5}i}{2} a=-\frac{\sqrt{5}i}{2}$$