Solve 25/16a^2=64

$$\frac { 25 } { 16 } a ^ { 2 } = 64$$

Solve for a

$$a = \frac{32}{5} = 6\frac{2}{5} = 6.4$$

$$a = -\frac{32}{5} = -6\frac{2}{5} = -6.4$$

Steps Using Difference of Squares

Multiply both sides by \frac{16}{25}, the reciprocal of \frac{25}{16}.

$$a^{2}=64\times \frac{16}{25}$$

Multiply 64 and \frac{16}{25} to get \frac{1024}{25}.

$$a^{2}=\frac{1024}{25}$$

Subtract \frac{1024}{25} from both sides.

$$a^{2}-\frac{1024}{25}=0$$

Multiply both sides by 25.

$$25a^{2}-1024=0$$

Consider 25a^{2}-1024. Rewrite 25a^{2}-1024 as \left(5a\right)^{2}-32^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5a-32\right)\left(5a+32\right)=0$$

To find equation solutions, solve 5a-32=0 and 5a+32=0.

$$a=\frac{32}{5} a=-\frac{32}{5}$$

Steps by Finding Square Root

Multiply both sides by \frac{16}{25}, the reciprocal of \frac{25}{16}.

$$a^{2}=64\times \frac{16}{25}$$

Multiply 64 and \frac{16}{25} to get \frac{1024}{25}.

$$a^{2}=\frac{1024}{25}$$

Take the square root of both sides of the equation.

$$a=\frac{32}{5} a=-\frac{32}{5}$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{16}{25}, the reciprocal of \frac{25}{16}.

$$a^{2}=64\times \frac{16}{25}$$

Multiply 64 and \frac{16}{25} to get \frac{1024}{25}.

$$a^{2}=\frac{1024}{25}$$

Subtract \frac{1024}{25} from both sides.

$$a^{2}-\frac{1024}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1024}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{1024}{25}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{1024}{25}\right)}}{2}$$

Multiply -4 times -\frac{1024}{25}.

$$a=\frac{0±\sqrt{\frac{4096}{25}}}{2}$$

Take the square root of \frac{4096}{25}.

$$a=\frac{0±\frac{64}{5}}{2}$$

Now solve the equation a=\frac{0±\frac{64}{5}}{2} when ± is plus.

$$a=\frac{32}{5}$$

Now solve the equation a=\frac{0±\frac{64}{5}}{2} when ± is minus.

$$a=-\frac{32}{5}$$

The equation is now solved.

$$a=\frac{32}{5} a=-\frac{32}{5}$$