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Solve the equation for s

64s^2+48s=-9
 

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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Your equation is equivalent to this equation:
64s2+48s+9=0;
 
I would like to show you here that this equation can be solved easily if you can observe something special about this equation.
 
64s2+48s+9=(8s)2+2*8s*3+32=(8s+3)2=0
 
The complete square equals zero if and only if the squared number is zero. Therefore, 
 
8s+3=0 or s=-3/8=-0.375

Comments

Thank you.  I noticed the squares in the equation, but I was struggling to figure out the answer