Solve the equation for s

Question

64s^2+48s=-9

 

Answer 1

64s² + 48s = -9

Add 9 to both sides of equation to obtain a quadratic equation = 0

64s² + 48s + 9 = 0

Factor the left side of equation:

(8s + 3)(8s + 3) =0

(8s + 3)² = 0

By the Zero Factor Theorem, if either factor is zero the product is zero and the equation is solved. Here both factors are the same, so there will only be one value for s.

8s + 3 =0

First subtract 3 from both sides of equation:

8s=-3

To further isolate the variable s, divide both sides of equation by 8:

s = - 3/8

Answer 2

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