Solve 4a^2=9/64

$$4 a ^ { 2 } = \frac { 9 } { 64 }$$

Solve for a

$$a=\frac{3}{16}=0.1875$$

$$a=-\frac{3}{16}=-0.1875$$

Steps Using Difference of Squares

Divide both sides by 4.

$$a^{2}=\frac{\frac{9}{64}}{4}$$

Express \frac{\frac{9}{64}}{4} as a single fraction.

$$a^{2}=\frac{9}{64\times 4}$$

Multiply 64 and 4 to get 256.

$$a^{2}=\frac{9}{256}$$

Subtract \frac{9}{256} from both sides.

$$a^{2}-\frac{9}{256}=0$$

Multiply both sides by 256.

$$256a^{2}-9=0$$

Consider 256a^{2}-9. Rewrite 256a^{2}-9 as \left(16a\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(16a-3\right)\left(16a+3\right)=0$$

To find equation solutions, solve 16a-3=0 and 16a+3=0.

$$a=\frac{3}{16} a=-\frac{3}{16}$$

Steps by Finding Square Root

Divide both sides by 4.

$$a^{2}=\frac{\frac{9}{64}}{4}$$

Express \frac{\frac{9}{64}}{4} as a single fraction.

$$a^{2}=\frac{9}{64\times 4}$$

Multiply 64 and 4 to get 256.

$$a^{2}=\frac{9}{256}$$

Take the square root of both sides of the equation.

$$a=\frac{3}{16} a=-\frac{3}{16}$$

Steps Using the Quadratic Formula

Divide both sides by 4.

$$a^{2}=\frac{\frac{9}{64}}{4}$$

Express \frac{\frac{9}{64}}{4} as a single fraction.

$$a^{2}=\frac{9}{64\times 4}$$

Multiply 64 and 4 to get 256.

$$a^{2}=\frac{9}{256}$$

Subtract \frac{9}{256} from both sides.

$$a^{2}-\frac{9}{256}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{256} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{256}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{9}{256}\right)}}{2}$$

Multiply -4 times -\frac{9}{256}.

$$a=\frac{0±\sqrt{\frac{9}{64}}}{2}$$

Take the square root of \frac{9}{64}.

$$a=\frac{0±\frac{3}{8}}{2}$$

Now solve the equation a=\frac{0±\frac{3}{8}}{2} when ± is plus.

$$a=\frac{3}{16}$$

Now solve the equation a=\frac{0±\frac{3}{8}}{2} when ± is minus.

$$a=-\frac{3}{16}$$

The equation is now solved.

$$a=\frac{3}{16} a=-\frac{3}{16}$$