Question

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

Answer 1

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(64x^2) = sqrt(9m^2)`
...giving:
`8x = 3m`

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

`x = (3m)/8`

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

`(8x)/3 = m`

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

GOOD LUCK

Answer 2

`x=+-(3m)/8`

Explanation:

`"rearrange and equate to zero"`

`64x^2-9m^2=0`

`"this is a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`64x^2=(8x)^2" and "9m^2=(3m)^2`

`rArra=8x" and "b=3m`

`rArr(8x-3m)(8x+3m)=0`

`"solving for x gives"`

`"equate each factor to zero and solve for x"`

`8x-3m=0rArrx=(3m)/8`

`8x+3m=0rArrx=-(3m)/8`