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

##### 2 Answers

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:

...giving:

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

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

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

GOOD LUCK

#### Explanation:

#"rearrange and equate to zero"#

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

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

#â€¢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#