# How do you solve 64x ^ { 2} = 9m^ { 2}?

Oct 31, 2017

If this is all the info you have, I don't believe you can "solve" it.

#### Explanation:

...it seems you have 2 unknowns, x and m. For 2 unknowns, you typically need 2 (linearly independent) equations, and you have only 1.

You can write an equation involving the square root of each of the terms in the given equation:

$\sqrt{64 {x}^{2}} = \sqrt{9 {m}^{2}}$
...giving:
$8 x = 3 m$

...then, you can write x as a function of m:

$x = \frac{3 m}{8}$

...or, you can write m as a function of x:

$\frac{8 x}{3} = m$

...but that's about as far as you can go with it.

GOOD LUCK

Oct 31, 2017

$x = \pm \frac{3 m}{8}$

#### Explanation:

$\text{rearrange and equate to zero}$

$64 {x}^{2} - 9 {m}^{2} = 0$

$\text{this is a "color(blue)"difference of squares}$

•color(white)(x)a^2-b^2=(a-b)(a+b)

$64 {x}^{2} = {\left(8 x\right)}^{2} \text{ and } 9 {m}^{2} = {\left(3 m\right)}^{2}$

$\Rightarrow a = 8 x \text{ and } b = 3 m$

$\Rightarrow \left(8 x - 3 m\right) \left(8 x + 3 m\right) = 0$

$\text{solving for x gives}$

$\text{equate each factor to zero and solve for x}$

$8 x - 3 m = 0 \Rightarrow x = \frac{3 m}{8}$

$8 x + 3 m = 0 \Rightarrow x = - \frac{3 m}{8}$